Q: What are the prime factors of the number 14,592?

 A: 2, 3, 19

Why are those the prime factors of the number 14,592?

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 14,592

14,592
Factor Arrows
27,296
Factor Arrows
23,648
Factor Arrows
21,824
Factor Arrows
2912
Factor Arrows
2456
Factor Arrows
2228
Factor Arrows
2114
Factor Arrows
257
Factor Arrows
319

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, 19

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 19 = 14,592

This can also be written as 28 x 31 x 191 = 14,592

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


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