Q: What are the prime factors of the number 30,520,314?

 A: 2, 3, 11, 173

Why are those the prime factors of the number 30,520,314?

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 30,520,314

30,520,314
Factor Arrows
215,260,157
Factor Arrows
35,086,719
Factor Arrows
31,695,573
Factor Arrows
3565,191
Factor Arrows
3188,397
Factor Arrows
362,799
Factor Arrows
320,933
Factor Arrows
111,903
Factor Arrows
11173

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, 11, 173

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 3 x 3 x 3 x 11 x 11 x 173 = 30,520,314

This can also be written as 21 x 36 x 112 x 1731 = 30,520,314

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


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