Q: What are the prime factors of the number 300,513,225?

 A: 3, 5, 29, 31, 4457

Why are those the prime factors of the number 300,513,225?

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 300,513,225

300,513,225
Factor Arrows
3100,171,075
Factor Arrows
520,034,215
Factor Arrows
54,006,843
Factor Arrows
29138,167
Factor Arrows
314,457

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, 29, 31, 4457

We can check our work by multiplying all of the prime factors together: 3 x 5 x 5 x 29 x 31 x 4,457 = 300,513,225

This can also be written as 31 x 52 x 291 x 311 x 4,4571 = 300,513,225

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


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