Q: What are the prime factors of the number 213,101,328?

 A: 2, 3, 11, 36691

Why are those the prime factors of the number 213,101,328?

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 213,101,328

213,101,328
Factor Arrows
2106,550,664
Factor Arrows
253,275,332
Factor Arrows
226,637,666
Factor Arrows
213,318,833
Factor Arrows
34,439,611
Factor Arrows
11403,601
Factor Arrows
1136,691

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, 36691

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 11 x 11 x 36,691 = 213,101,328

This can also be written as 24 x 31 x 112 x 36,6911 = 213,101,328

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


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