Q: What are the prime factors of the number 31,435,209?

 A: 3, 13, 31, 107

Why are those the prime factors of the number 31,435,209?

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 31,435,209

31,435,209
Factor Arrows
310,478,403
Factor Arrows
33,492,801
Factor Arrows
31,164,267
Factor Arrows
3388,089
Factor Arrows
3129,363
Factor Arrows
343,121
Factor Arrows
133,317
Factor Arrows
31107

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, 13, 31, 107

We can check our work by multiplying all of the prime factors together: 3 x 3 x 3 x 3 x 3 x 3 x 13 x 31 x 107 = 31,435,209

This can also be written as 36 x 131 x 311 x 1071 = 31,435,209

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


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