Q: What are the prime factors of the number 686,816?

 A: 2, 13, 127

Why are those the prime factors of the number 686,816?

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 686,816

686,816
Factor Arrows
2343,408
Factor Arrows
2171,704
Factor Arrows
285,852
Factor Arrows
242,926
Factor Arrows
221,463
Factor Arrows
131,651
Factor Arrows
13127

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, 13, 127

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 13 x 13 x 127 = 686,816

This can also be written as 25 x 132 x 1271 = 686,816

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


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