Q: What are the prime factors of the number 813,456?

 A: 2, 3, 7, 269

Why are those the prime factors of the number 813,456?

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 813,456

813,456
Factor Arrows
2406,728
Factor Arrows
2203,364
Factor Arrows
2101,682
Factor Arrows
250,841
Factor Arrows
316,947
Factor Arrows
35,649
Factor Arrows
31,883
Factor Arrows
7269

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, 269

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 269 = 813,456

This can also be written as 24 x 33 x 71 x 2691 = 813,456

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


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