Q: What are the prime factors of the number 253,151,325?

 A: 3, 5, 7, 5953

Why are those the prime factors of the number 253,151,325?

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 253,151,325

253,151,325
Factor Arrows
384,383,775
Factor Arrows
328,127,925
Factor Arrows
39,375,975
Factor Arrows
33,125,325
Factor Arrows
31,041,775
Factor Arrows
5208,355
Factor Arrows
541,671
Factor Arrows
75,953

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:

3, 5, 7, 5953

We can check our work by multiplying all of the prime factors together: 3 x 3 x 3 x 3 x 3 x 5 x 5 x 7 x 5,953 = 253,151,325

This can also be written as 35 x 52 x 71 x 5,9531 = 253,151,325

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


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