- The product of a number times an integer is a multiple of that number
- Example: 2 * 3 = 6 and 3 * 2 = 6, as a result, 6 is a multiple of 2 and 3
- 0 (zero) is a multiple of all numbers since the product of 0 times another number equals 0
- Multiples can also be negative (less than 0) since the product of a negative number times a positive number is negative
- Multiples of 2 are even numbers, 2, 4, 6, 8, 10, 12, …
- If the sum of the digits in an integer is divisible by 3, then that integer is a multiple of 3
- Multiples of 5 end with a 0 or 5
- Multiples of 10 end with a 0
- The Least Common Multiple (LCM) of two or more numbers could be determined by listing their multiples
- Nonzero numbers have an infinite number of multiples in contrast to a finite number of factors
| Look up multiple or submultiple in Wiktionary, the free dictionary. |
In science, a multiple is the product of any quantity and an integer. In other words, for the quantities a and b, we say 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 is an integer.
In mathematics, 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 "b being an integer multiple of a". This terminology is also used with units of measurement (for example by the BIPM and NIST), 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 103. For example, a millimetre is the 1000-fold submultiple of a metre. As another example, one inch may be considered as a 12-fold submultiple of a foot, or a 36-fold submultiple of a yard.