Q: What are the prime factors of the number 31,465,200?

 A: 2, 3, 5, 13, 2017

Why are those the prime factors of the number 31,465,200?

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 31,465,200

31,465,200
Factor Arrows
215,732,600
Factor Arrows
27,866,300
Factor Arrows
23,933,150
Factor Arrows
21,966,575
Factor Arrows
3655,525
Factor Arrows
5131,105
Factor Arrows
526,221
Factor Arrows
132,017

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, 13, 2017

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13 x 2,017 = 31,465,200

This can also be written as 24 x 31 x 52 x 131 x 2,0171 = 31,465,200

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


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