Q: What are the prime factors of the number 405,867,105?

 A: 3, 5, 7, 15907

Why are those the prime factors of the number 405,867,105?

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 405,867,105

405,867,105
Factor Arrows
3135,289,035
Factor Arrows
345,096,345
Factor Arrows
315,032,115
Factor Arrows
35,010,705
Factor Arrows
31,670,235
Factor Arrows
3556,745
Factor Arrows
5111,349
Factor Arrows
715,907

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, 15907

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 5 x 7 x 15,907 = 405,867,105

This can also be written as 36 x 51 x 71 x 15,9071 = 405,867,105

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


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