Q: What are the prime factors of the number 333,072?

 A: 2, 3, 257

Why are those the prime factors of the number 333,072?

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 333,072

333,072
Factor Arrows
2166,536
Factor Arrows
283,268
Factor Arrows
241,634
Factor Arrows
220,817
Factor Arrows
36,939
Factor Arrows
32,313
Factor Arrows
3771
Factor Arrows
3257

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, 257

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 257 = 333,072

This can also be written as 24 x 34 x 2571 = 333,072

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


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