Q: What are the prime factors of the number 221,102,640?

 A: 2, 3, 5, 11, 27917

Why are those the prime factors of the number 221,102,640?

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 221,102,640

221,102,640
Factor Arrows
2110,551,320
Factor Arrows
255,275,660
Factor Arrows
227,637,830
Factor Arrows
213,818,915
Factor Arrows
34,606,305
Factor Arrows
31,535,435
Factor Arrows
5307,087
Factor Arrows
1127,917

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, 11, 27917

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11 x 27,917 = 221,102,640

This can also be written as 24 x 32 x 51 x 111 x 27,9171 = 221,102,640

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


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