Q: What are the prime factors of the number 305,332,524?

 A: 2, 3, 7, 57697

Why are those the prime factors of the number 305,332,524?

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 305,332,524

305,332,524
Factor Arrows
2152,666,262
Factor Arrows
276,333,131
Factor Arrows
325,444,377
Factor Arrows
38,481,459
Factor Arrows
32,827,153
Factor Arrows
7403,879
Factor Arrows
757,697

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, 57697

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 7 x 57,697 = 305,332,524

This can also be written as 22 x 33 x 72 x 57,6971 = 305,332,524

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


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