Q: What are the prime factors of the number 433,872?

 A: 2, 3, 23, 131

Why are those the prime factors of the number 433,872?

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 433,872

433,872
Factor Arrows
2216,936
Factor Arrows
2108,468
Factor Arrows
254,234
Factor Arrows
227,117
Factor Arrows
39,039
Factor Arrows
33,013
Factor Arrows
23131

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, 23, 131

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 23 x 131 = 433,872

This can also be written as 24 x 32 x 231 x 1311 = 433,872

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


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