Q: What are the prime factors of the number 43,164?

 A: 2, 3, 11, 109

Why are those the prime factors of the number 43,164?

Prime factors are the prime numbers that can be multipled together to equal the original number. You find the factors by dividing by prime numbers. It is best shown by creating a Factor Tree.

Factor Tree for the number 43,164

43,164
Factor Arrows
221,582
Factor Arrows
210,791
Factor Arrows
33,597
Factor Arrows
31,199
Factor Arrows
11109

The numbers in bold above are the prime factors. If there are multiples, you only count them one time. This leads us to our prime factors of:

2, 3, 11, 109

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 11 x 109 = 43,164

This can also be written as 22 x 32 x 111 x 1091 = 43,164

If you would like to know more, or need additional explanation, please review our prime factorization explanation.


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