Q: What are the prime factors of the number 577,125?

 A: 3, 5, 19

Why are those the prime factors of the number 577,125?

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 577,125

577,125
Factor Arrows
3192,375
Factor Arrows
364,125
Factor Arrows
321,375
Factor Arrows
37,125
Factor Arrows
32,375
Factor Arrows
5475
Factor Arrows
595
Factor Arrows
519

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, 19

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 5 x 19 = 577,125

This can also be written as 35 x 53 x 191 = 577,125

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


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