Multiple

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In mathematics, a multiple is the product of any quantity by an integer.^[1][2][3] In other words, for the quantity a such as integer, real number, or complex number, b is a multiple of a if b = na for some integer n. The n is also called coefficient or multiplier. Additionally, if a is not zero, this is equivalent to saying that b / a is an integer with no remainder.^[4][5][6]

Some said the multiple is the product of an integer by another integer^[7] so it is called integer multiple. When a and b are both integers, a is also called a factor of b.

Examples

14, 49 , -21 and 0 are multiples of 7 whereas 3 and -6 are not. This is because there are integers that 7 may be multiplied by to reach the values of 14, 49, 0, and -21, while there are no such integers for 3 and -6. Each of the products listed below, and in particular, the products for 3 and -6, is the only way that the relevant number can be written as a product of 7 and another real number:

• ;
• ;
• ;
• ;
• , and 3 / 7 is a fraction, not an integer;
• , and − 6 / 7 is a fraction, not an integer.

Properties

• 0 is a multiple of everything ().
• The product of any integer n and any integer is a multiple of n. In particular, n, which is equal to , is a multiple of n (every integer is a multiple of itself), since 1 is an integer.
• If a and b are multiples of x, then a + b, a − b, (p − 0)! + 0 is a multiple of p.

References

1. ^ Weisstein, Eric W., "Multiple" from MathWorld.
2. ^ WordNet lexicon database, Princeton University
3. ^ WordReference.com
4. ^ The Free Dictionary by Farlex
5. ^ Dictionary.com Unabridged
6. ^ Cambridge Dictionary Online
7. ^ Mathematics Glossary: Voluntary Stat Cirriculum

See also

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