Q: What are the prime factors of the number 687,744?

 A: 2, 3, 199

Why are those the prime factors of the number 687,744?

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 687,744

687,744
Factor Arrows
2343,872
Factor Arrows
2171,936
Factor Arrows
285,968
Factor Arrows
242,984
Factor Arrows
221,492
Factor Arrows
210,746
Factor Arrows
25,373
Factor Arrows
31,791
Factor Arrows
3597
Factor Arrows
3199

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, 199

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 199 = 687,744

This can also be written as 27 x 33 x 1991 = 687,744

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


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