What Is a Factor Pair in Math?

A factor pair is a pair of integers whose product is a given number. The factors of a prime number are only 1 and itself. Composite numbers have the factor pair of 1 and itself, as well as at least one other factor pair.

The first positive prime number with a factor pair of only 1 and itself is 2. The number 1 is not considered a prime number, despite the fact that it could be interpreted as having the same property. Above 2, all prime numbers are odd. Every even number is divisible by 2 and half its value, and so each has at least two factor pairs. If negative numbers are included in the factorization, the number of factor pairs is doubled. Take for example that 2 also has the factor pair of -2 and -1.

Note that only integers, numbers that are whole number multiples of 1 or -1, have factor pairs. Other numbers on the real number line that have values between two integers are not considered to have factor pairs. The only number with infinite factors is 0, and it is the only number with 0 as a factor. All factor pairs of 0 include 0 as one of the factors.