Q: What are the prime factors of the number 45,900?

 A: 2, 3, 5, 17

Why are those the prime factors of the number 45,900?

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 45,900

45,900
Factor Arrows
222,950
Factor Arrows
211,475
Factor Arrows
33,825
Factor Arrows
31,275
Factor Arrows
3425
Factor Arrows
585
Factor Arrows
517

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, 5, 17

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 3 x 5 x 5 x 17 = 45,900

This can also be written as 22 x 33 x 52 x 171 = 45,900

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


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