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# 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.

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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.

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## Related Questions

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To factor the difference of two squares, break down the squares, and then factor them out to get the positive and negative solutions. The proper solution includes the sum and the difference of the two square roots, multiplied together.

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The difference of 9 and the quotient of a number T and 6 which equals 5 is either 21 or -21. When T/6 = 5, basic algebra gives the formula T = 6 * 5, which gives T = 30.

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An integer is a whole number that is not a fraction. Integers include both positive and negative numbers, and there are several rules for adding integers.