# What Is a Prime Factor in Mathematics?

Prime numbers that, when multiplied, equal another number are said to be the “prime factors” of that number. For example, 2 and 7 are the prime factors of the number 14.

A prime number can only be multiplied by itself and the number 1. So, the number “8” is not prime because it’s possible to multiply “2” and “4” to produce the number 8. The number “7” is prime because no other whole numbers produce the number when multiplied together besides itself and the number 1. Determining prime factors of a number means breaking this number up into more numbers and then checking to see if those new numbers are prime. For example, the number “32” can be broken up into “8” and “4,” which when multiplied together make 32. But “8” and “4” aren’t prime numbers themselves. It’s necessary to break these numbers down further before they are prime factors. In this case, it takes four of the number “2” to make up the prime factors of number “32.” It’s also possible to write prime factors with an exponent if they include multiple of the same number. For example, the prime factors of 32 include “2” with an exponent of “4.”

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