Factor Pair Calculator

Finding the factor pairs of a number is useful when deciding how to divide a quantity into equal pieces, or when choosing how to parcel quantities of a product. For example, a food company that makes frozen chicken patties may choose sell by the dozen, since 12 is divisible by 2, 3, 4, and 6, thus making it easy to feed a family of various sizes. The factor pairs of 12 are (1, 12), (2, 6) and (3, 4). You can use the calculator on the left to quickly generate a list of factors pairs for a given number.

How to Find Factor Pairs by Hand

A typical math homework question in lower and middle grades is to find all the factor pairs of a given number. To do this by hand, you must check all the possible divisors up to the square root of the given number.

For example, suppose you wish to group the divisors of 396 into pairs. Since sqrt(396) is less than 20 (since 20 squared equals 400), you only need to check the numbers up to 19. The first pair is

(1, 396)

Next, a quick check of divisibility rules will reveal that 396 is divisible by 2, 3, 4, 6, 9, 11, 12, and 18 and no other numbers. When you divide 396 by each of these numbers, you get the other half of the factor pair. Thus, the remaining factor pairs are

(2, 198)
(3, 132)
(4, 99)
(6, 66)
(9, 44)
(11, 36)
(12, 33)
(18, 22)

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