Q: What are the prime factors of the number 428,085?

 A: 3, 5, 7, 151

Why are those the prime factors of the number 428,085?

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 428,085

428,085
Factor Arrows
3142,695
Factor Arrows
347,565
Factor Arrows
315,855
Factor Arrows
35,285
Factor Arrows
51,057
Factor Arrows
7151

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:

3, 5, 7, 151

We can check our work by multiplying all of the prime factors together: 3 x 3 x 3 x 3 x 5 x 7 x 151 = 428,085

This can also be written as 34 x 51 x 71 x 1511 = 428,085

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


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