# Trait num_integer::Integer

``````pub trait Integer: Sized + Num + PartialOrd + Ord + Eq {
Show 16 methods    // Required methods
fn div_floor(&self, other: &Self) -> Self;
fn mod_floor(&self, other: &Self) -> Self;
fn gcd(&self, other: &Self) -> Self;
fn lcm(&self, other: &Self) -> Self;
fn divides(&self, other: &Self) -> bool;
fn is_multiple_of(&self, other: &Self) -> bool;
fn is_even(&self) -> bool;
fn is_odd(&self) -> bool;
fn div_rem(&self, other: &Self) -> (Self, Self);

// Provided methods
fn div_ceil(&self, other: &Self) -> Self { ... }
fn gcd_lcm(&self, other: &Self) -> (Self, Self) { ... }
fn extended_gcd(&self, other: &Self) -> ExtendedGcd<Self>
where Self: Clone { ... }
fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)
where Self: Clone + Signed { ... }
fn div_mod_floor(&self, other: &Self) -> (Self, Self) { ... }
fn next_multiple_of(&self, other: &Self) -> Self
where Self: Clone { ... }
fn prev_multiple_of(&self, other: &Self) -> Self
where Self: Clone { ... }
}``````

## Required Methods§

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#### fn div_floor(&self, other: &Self) -> Self

Floored integer division.

##### Examples
``````assert!(( 8).div_floor(& 3) ==  2);
assert!(( 8).div_floor(&-3) == -3);
assert!((-8).div_floor(& 3) == -3);
assert!((-8).div_floor(&-3) ==  2);

assert!(( 1).div_floor(& 2) ==  0);
assert!(( 1).div_floor(&-2) == -1);
assert!((-1).div_floor(& 2) == -1);
assert!((-1).div_floor(&-2) ==  0);``````
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#### fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo, satisfying:

``assert!(n.div_floor(&d) * d + n.mod_floor(&d) == n)``
##### Examples
``````assert!(( 8).mod_floor(& 3) ==  2);
assert!(( 8).mod_floor(&-3) == -1);
assert!((-8).mod_floor(& 3) ==  1);
assert!((-8).mod_floor(&-3) == -2);

assert!(( 1).mod_floor(& 2) ==  1);
assert!(( 1).mod_floor(&-2) == -1);
assert!((-1).mod_floor(& 2) ==  1);
assert!((-1).mod_floor(&-2) == -1);``````
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#### fn gcd(&self, other: &Self) -> Self

Greatest Common Divisor (GCD).

##### Examples
``````assert_eq!(6.gcd(&8), 2);
assert_eq!(7.gcd(&3), 1);``````
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#### fn lcm(&self, other: &Self) -> Self

Lowest Common Multiple (LCM).

##### Examples
``````assert_eq!(7.lcm(&3), 21);
assert_eq!(2.lcm(&4), 4);
assert_eq!(0.lcm(&0), 0);``````
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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if `self` is a multiple of `other`.

##### Examples
``````assert_eq!(9.is_multiple_of(&3), true);
assert_eq!(3.is_multiple_of(&9), false);``````
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#### fn is_even(&self) -> bool

Returns `true` if the number is even.

##### Examples
``````assert_eq!(3.is_even(), false);
assert_eq!(4.is_even(), true);``````
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#### fn is_odd(&self) -> bool

Returns `true` if the number is odd.

##### Examples
``````assert_eq!(3.is_odd(), true);
assert_eq!(4.is_odd(), false);``````
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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus. Returns `(quotient, remainder)`.

##### Examples
``````assert_eq!(( 8).div_rem( &3), ( 2,  2));
assert_eq!(( 8).div_rem(&-3), (-2,  2));
assert_eq!((-8).div_rem( &3), (-2, -2));
assert_eq!((-8).div_rem(&-3), ( 2, -2));

assert_eq!(( 1).div_rem( &2), ( 0,  1));
assert_eq!(( 1).div_rem(&-2), ( 0,  1));
assert_eq!((-1).div_rem( &2), ( 0, -1));
assert_eq!((-1).div_rem(&-2), ( 0, -1));``````

## Provided Methods§

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#### fn div_ceil(&self, other: &Self) -> Self

Ceiled integer division.

##### Examples
``````assert_eq!(( 8).div_ceil( &3),  3);
assert_eq!(( 8).div_ceil(&-3), -2);
assert_eq!((-8).div_ceil( &3), -2);
assert_eq!((-8).div_ceil(&-3),  3);

assert_eq!(( 1).div_ceil( &2), 1);
assert_eq!(( 1).div_ceil(&-2), 0);
assert_eq!((-1).div_ceil( &2), 0);
assert_eq!((-1).div_ceil(&-2), 1);``````
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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) together.

Potentially more efficient than calling `gcd` and `lcm` individually for identical inputs.

##### Examples
``````assert_eq!(10.gcd_lcm(&4), (2, 20));
assert_eq!(8.gcd_lcm(&9), (1, 72));``````
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#### fn extended_gcd(&self, other: &Self) -> ExtendedGcd<Self>where Self: Clone,

Greatest common divisor and Bézout coefficients.

##### Examples
``````fn check<A: Copy + Integer + NumAssign>(a: A, b: A) -> bool {
let ExtendedGcd { gcd, x, y, .. } = a.extended_gcd(&b);
gcd == x * a + y * b
}
assert!(check(10isize, 4isize));
assert!(check(8isize,  9isize));``````
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#### fn extended_gcd_lcm(&self, other: &Self) -> (ExtendedGcd<Self>, Self)where Self: Clone + Signed,

Greatest common divisor, least common multiple, and Bézout coefficients.

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#### fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Simultaneous floored integer division and modulus. Returns `(quotient, remainder)`.

##### Examples
``````assert_eq!(( 8).div_mod_floor( &3), ( 2,  2));
assert_eq!(( 8).div_mod_floor(&-3), (-3, -1));
assert_eq!((-8).div_mod_floor( &3), (-3,  1));
assert_eq!((-8).div_mod_floor(&-3), ( 2, -2));

assert_eq!(( 1).div_mod_floor( &2), ( 0,  1));
assert_eq!(( 1).div_mod_floor(&-2), (-1, -1));
assert_eq!((-1).div_mod_floor( &2), (-1,  1));
assert_eq!((-1).div_mod_floor(&-2), ( 0, -1));``````
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#### fn next_multiple_of(&self, other: &Self) -> Selfwhere Self: Clone,

Rounds up to nearest multiple of argument.

##### Notes

For signed types, `a.next_multiple_of(b) = a.prev_multiple_of(b.neg())`.

##### Examples
``````assert_eq!(( 16).next_multiple_of(& 8),  16);
assert_eq!(( 23).next_multiple_of(& 8),  24);
assert_eq!(( 16).next_multiple_of(&-8),  16);
assert_eq!(( 23).next_multiple_of(&-8),  16);
assert_eq!((-16).next_multiple_of(& 8), -16);
assert_eq!((-23).next_multiple_of(& 8), -16);
assert_eq!((-16).next_multiple_of(&-8), -16);
assert_eq!((-23).next_multiple_of(&-8), -24);``````
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#### fn prev_multiple_of(&self, other: &Self) -> Selfwhere Self: Clone,

Rounds down to nearest multiple of argument.

##### Notes

For signed types, `a.prev_multiple_of(b) = a.next_multiple_of(b.neg())`.

##### Examples
``````assert_eq!(( 16).prev_multiple_of(& 8),  16);
assert_eq!(( 23).prev_multiple_of(& 8),  16);
assert_eq!(( 16).prev_multiple_of(&-8),  16);
assert_eq!(( 23).prev_multiple_of(&-8),  24);
assert_eq!((-16).prev_multiple_of(& 8), -16);
assert_eq!((-23).prev_multiple_of(& 8), -24);
assert_eq!((-16).prev_multiple_of(&-8), -16);
assert_eq!((-23).prev_multiple_of(&-8), -16);``````

## Implementations on Foreign Types§

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### impl Integer for usize

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#### fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as `div` (`/`).

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#### fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as `rem` (`%`).

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`.

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`.

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for isize

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#### fn div_floor(&self, other: &Self) -> Self

Floored integer division

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#### fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

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#### fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates `div_floor` and `mod_floor` simultaneously

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`. The result is always positive.

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for u16

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#### fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as `div` (`/`).

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#### fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as `rem` (`%`).

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`.

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`.

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for i64

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#### fn div_floor(&self, other: &Self) -> Self

Floored integer division

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#### fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

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#### fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates `div_floor` and `mod_floor` simultaneously

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`. The result is always positive.

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for u64

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#### fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as `div` (`/`).

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#### fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as `rem` (`%`).

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`.

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`.

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for i16

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#### fn div_floor(&self, other: &Self) -> Self

Floored integer division

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#### fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

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#### fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates `div_floor` and `mod_floor` simultaneously

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`. The result is always positive.

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for i128

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#### fn div_floor(&self, other: &Self) -> Self

Floored integer division

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#### fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

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#### fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates `div_floor` and `mod_floor` simultaneously

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`. The result is always positive.

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for i32

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#### fn div_floor(&self, other: &Self) -> Self

Floored integer division

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#### fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

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#### fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates `div_floor` and `mod_floor` simultaneously

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`. The result is always positive.

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for u8

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#### fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as `div` (`/`).

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#### fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as `rem` (`%`).

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`.

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`.

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for u128

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#### fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as `div` (`/`).

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#### fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as `rem` (`%`).

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`.

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`.

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for i8

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#### fn div_floor(&self, other: &Self) -> Self

Floored integer division

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#### fn mod_floor(&self, other: &Self) -> Self

Floored integer modulo

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#### fn div_mod_floor(&self, other: &Self) -> (Self, Self)

Calculates `div_floor` and `mod_floor` simultaneously

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`. The result is always positive.

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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### impl Integer for u32

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#### fn div_floor(&self, other: &Self) -> Self

Unsigned integer division. Returns the same result as `div` (`/`).

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#### fn mod_floor(&self, other: &Self) -> Self

Unsigned integer modulo operation. Returns the same result as `rem` (`%`).

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#### fn gcd(&self, other: &Self) -> Self

Calculates the Greatest Common Divisor (GCD) of the number and `other`

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#### fn lcm(&self, other: &Self) -> Self

Calculates the Lowest Common Multiple (LCM) of the number and `other`.

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#### fn gcd_lcm(&self, other: &Self) -> (Self, Self)

Calculates the Greatest Common Divisor (GCD) and Lowest Common Multiple (LCM) of the number and `other`.

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#### fn divides(&self, other: &Self) -> bool

Deprecated, use `is_multiple_of` instead.

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#### fn is_multiple_of(&self, other: &Self) -> bool

Returns `true` if the number is a multiple of `other`.

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#### fn is_even(&self) -> bool

Returns `true` if the number is divisible by `2`.

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#### fn is_odd(&self) -> bool

Returns `true` if the number is not divisible by `2`.

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#### fn div_rem(&self, other: &Self) -> (Self, Self)

Simultaneous truncated integer division and modulus.

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