English

Noun

1. An integer that is an exact divisor or another

Translations

In mathematics, a multiple of an integer is the product of that integer with another integer. In other words, a is a multiple of b if a=nb, where n is an integer. If b is not zero, this is equivalent to saying that a/b is an integer.

Examples

• 14, 49, and 21 are multiples of 7 whereas 3, 15, and 20 are not.

Properties

• Every number is a multiple of itself (b=1\cdot b ).
• 0 is a multiple of every integer (0=0\cdot b ).
• A multiple of a number is obtained by multiplying the number by any natural number.
• If a and b are multiples of x, then a+b, a-b and ab are multiples of x.
• For any integer p > 1, (p-1)!+1 is a multiple of p if and only if p is a prime number (Wilson's theorem).

See also

• Divisor
• Ideal (ring theory)
• Decimal and SI prefix