Abstraction of integral numeric types. That is, types with no fractional part, including `Integer`.

The division operation for integral numeric types results in a remainder. Therefore, integral numeric types have an operation, denoted by the remainder operator `%`, to determine the remainder of any division operation.

```if (n%2==0) {
print("Even!");
}
```

Division and the remainder operation should satisfy:

• `x == (x/y)*y + x%y`

for any instance `y` other than `0`.

All `Integral` numeric types are also `Enumerable`, so ranges of integral values may be produced using the `measure()` and `span()` operators.

```// Iterate from 0 to 100 inclusive
for (i in 0..100) {
print("The square of ``i`` is ``i^2``");
}

// Iterate all indices of the array,
// from 0 to array.size-1
for (i in 0:array.size) {
print(array[i]);
}
```
By: Gavin
See also `Integer`

no type hierarchy

• `Integral`
• `Enumerable`
• `Ordinal`
• `Number`
• `Comparable`
• `Numeric`
• `Invertible`
• `Summable`
• `Integral` of
• `Integer`
 Attributes `unit` Source Code`shared formal Boolean unit`Determine if the number is the multiplicative identity. `zero` Source Code`shared formal Boolean zero`Determine if the number is the additive identity.
 Inherited Attributes Attributes inherited from: `Object` Attributes inherited from: `Enumerable` Attributes inherited from: `Invertible``negated` Attributes inherited from: `Number` Attributes inherited from: `Ordinal`
 Methods `divides` Source Code`shared default Boolean divides(Other other)`Determine if this number is a factor of the given number. `modulo` Source Code`shared default Other modulo(Other modulus)`The modulo, after dividing this number by the given number. This differs from `remainder()` in that the result is always positive. Throws `AssertionError`If the modulus is not strictly positive `remainder` Source Code`shared formal Other remainder(Other other)`The remainder, after dividing this number by the given number.
 Inherited Methods Methods inherited from: `Object``equals()` Methods inherited from: `Comparable` Methods inherited from: `Enumerable` Methods inherited from: `Invertible``minus()` Methods inherited from: `Number` Methods inherited from: `Numeric` Methods inherited from: `Summable``plus()`