Q: What are the prime factors of the number 400,116,165?

 A: 3, 5, 17, 23, 4013

Why are those the prime factors of the number 400,116,165?

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 400,116,165

400,116,165
Factor Arrows
3133,372,055
Factor Arrows
526,674,411
Factor Arrows
171,569,083
Factor Arrows
1792,299
Factor Arrows
234,013

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, 17, 23, 4013

We can check our work by multiplying all of the prime factors together: 3 x 5 x 17 x 17 x 23 x 4,013 = 400,116,165

This can also be written as 31 x 51 x 172 x 231 x 4,0131 = 400,116,165

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


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