Q: What are the prime factors of the number 333,002,124?

 A: 2, 3, 7, 13, 31, 1093

Why are those the prime factors of the number 333,002,124?

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 333,002,124

333,002,124
Factor Arrows
2166,501,062
Factor Arrows
283,250,531
Factor Arrows
327,750,177
Factor Arrows
39,250,059
Factor Arrows
33,083,353
Factor Arrows
7440,479
Factor Arrows
1333,883
Factor Arrows
311,093

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, 7, 13, 31, 1093

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 3 x 7 x 13 x 31 x 1,093 = 333,002,124

This can also be written as 22 x 33 x 71 x 131 x 311 x 1,0931 = 333,002,124

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


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