# Multiple (mathematics)

In mathematics, a **multiple** is the product of any quantity and an integer.[1] In other words, for the quantities *a* and *b*, it can be said that *b* is a multiple of *a* if *b* = *na* for some integer *n*, which is called the multiplier. If *a* is not zero, this is equivalent to saying that is an integer.

When *a* and *b* are both integers, and *b* is a multiple of *a*, then *a* is called a divisor of *b*. One says also that *a* divides *b*. If *a* and *b* are not integers, mathematicians prefer generally to use **integer multiple** instead of *multiple*, for clarification. In fact, *multiple* is used for other kinds of product; for example, a polynomial *p* is a multiple of another polynomial *q* if there exists third polynomial *r* such that *p* = *qr*.

In some texts, "*a* is a **submultiple** of *b*" has the meaning of "*a* being a unit fraction of *b*" or, equivalently, "*b* being an integer multiple of *a*". This terminology is also used with units of measurement (for example by the BIPM[2] and NIST[3]), where a *submultiple* of a main unit is a unit, named by prefixing the main unit, defined as the quotient of the main unit by an integer, mostly a power of 10^{3}. For example, a millimetre is the 1000-fold submultiple of a metre.[2][3] As another example, one inch may be considered as a 12-fold submultiple of a foot, or a 36-fold submultiple of a yard.