Q: What are the prime factors of the number 33,123,330?

 A: 2, 3, 5, 43, 317

Why are those the prime factors of the number 33,123,330?

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 33,123,330

33,123,330
Factor Arrows
216,561,665
Factor Arrows
35,520,555
Factor Arrows
31,840,185
Factor Arrows
3613,395
Factor Arrows
3204,465
Factor Arrows
368,155
Factor Arrows
513,631
Factor Arrows
43317

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, 43, 317

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 5 x 43 x 317 = 33,123,330

This can also be written as 21 x 35 x 51 x 431 x 3171 = 33,123,330

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


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