Q: What are the prime factors of the number 333,343,200?

 A: 2, 3, 5, 138893

Why are those the prime factors of the number 333,343,200?

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 333,343,200

333,343,200
Factor Arrows
2166,671,600
Factor Arrows
283,335,800
Factor Arrows
241,667,900
Factor Arrows
220,833,950
Factor Arrows
210,416,975
Factor Arrows
33,472,325
Factor Arrows
5694,465
Factor Arrows
5138,893

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, 138893

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 5 x 5 x 138,893 = 333,343,200

This can also be written as 25 x 31 x 52 x 138,8931 = 333,343,200

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


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