What Is the Difference Between a Factor and a Multiple?

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The factors of a number are all the integers that can be multiplied together to produce that number. For example, 1, 2, 3 and 6 are all factors of 6. Multiples are all the numbers of which a given number is a factor.

The possible multiples of any number are unlimited. For example, the multiples of 5 are all the numbers produced by multiplying 5 by another number, such as 5, 10, 15 or 20, which is an infinite series. While factors must be integers, multiples can be any kind of number. For example, 12(pi) is a multiple of both 12 and pi. A number that has no factors other than one and itself is called a prime number.