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# What is a prime factor in mathematics?

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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.

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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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## Related Questions

• A:

Eighty-nine is a prime number. To check for a prime number, divide it by every number from two to one less than the number (88 in this case). If no smaller number can be evenly divided into the number, which is the case for 88,Â then it is prime.

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• A:

Two is the only even prime number because other even numbers have at least three or more positive divisors. A number can only be considered prime when it only has two positive divisors: itself and 1.

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The number 87 is not a prime number. The factors of 87 are 1, 3 and 29. A prime number must have only two factors, the numbers one and the number itself.