Q: What are the prime factors of the number 311,640?

 A: 2, 3, 5, 7, 53

Why are those the prime factors of the number 311,640?

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 311,640

311,640
Factor Arrows
2155,820
Factor Arrows
277,910
Factor Arrows
238,955
Factor Arrows
312,985
Factor Arrows
52,597
Factor Arrows
7371
Factor Arrows
753

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, 5, 7, 53

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 5 x 7 x 7 x 53 = 311,640

This can also be written as 23 x 31 x 51 x 72 x 531 = 311,640

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


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