Q: What are the prime factors of the number 5,909,625?

 A: 3, 5, 17, 103

Why are those the prime factors of the number 5,909,625?

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 5,909,625

5,909,625
Factor Arrows
31,969,875
Factor Arrows
3656,625
Factor Arrows
3218,875
Factor Arrows
543,775
Factor Arrows
58,755
Factor Arrows
51,751
Factor Arrows
17103

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, 17, 103

We can check our work by multiplying all of the prime factors together: 3 x 3 x 3 x 5 x 5 x 5 x 17 x 103 = 5,909,625

This can also be written as 33 x 53 x 171 x 1031 = 5,909,625

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


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