Q: What are the prime factors of the number 333,412,128?

 A: 2, 3, 7, 165383

Why are those the prime factors of the number 333,412,128?

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 333,412,128

333,412,128
Factor Arrows
2166,706,064
Factor Arrows
283,353,032
Factor Arrows
241,676,516
Factor Arrows
220,838,258
Factor Arrows
210,419,129
Factor Arrows
33,473,043
Factor Arrows
31,157,681
Factor Arrows
7165,383

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, 165383

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 x 165,383 = 333,412,128

This can also be written as 25 x 32 x 71 x 165,3831 = 333,412,128

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


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