Q: What are the prime factors of the number 678,016?

 A: 2, 5297

Why are those the prime factors of the number 678,016?

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 678,016

678,016
Factor Arrows
2339,008
Factor Arrows
2169,504
Factor Arrows
284,752
Factor Arrows
242,376
Factor Arrows
221,188
Factor Arrows
210,594
Factor Arrows
25,297

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, 5297

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 5,297 = 678,016

This can also be written as 27 x 5,2971 = 678,016

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


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