Q: What are the prime factors of the number 723,492?

 A: 2, 3, 7, 11, 29

Why are those the prime factors of the number 723,492?

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 723,492

723,492
Factor Arrows
2361,746
Factor Arrows
2180,873
Factor Arrows
360,291
Factor Arrows
320,097
Factor Arrows
36,699
Factor Arrows
32,233
Factor Arrows
7319
Factor Arrows
1129

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, 11, 29

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 3 x 3 x 7 x 11 x 29 = 723,492

This can also be written as 22 x 34 x 71 x 111 x 291 = 723,492

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


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