In mathematics, a multiple is the product of any quantity and an integer. 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
b/a
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.
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:
14=7 x 2;
49=7 x 7;
-21=7 x (-3);
0=7 x 0;
3=7 x (3/7), 3/7
-6=7 x (-6/7), -6/7
0=0 ⋅ b
n
n
n
n x 1
n
a
b
x,
a+b
a-b
x
In some texts, "a is a submultiple of b" has the meaning of "a being a unit fraction of b" (a1/b) or, equivalently, "b being an integer multiple n of a" (bna). This terminology is also used with units of measurement (for example by the BIPM and NIST), where a unit submultiple is obtained by prefixing the main unit, defined as the quotient of the main unit by an integer, mostly a power of 103. For example, a millimetre is the 1000-fold submultiple of a metre.[1] [2] As another example, one inch may be considered as a 12-fold submultiple of a foot, or a 36-fold submultiple of a yard.