Q: What are the prime factors of the number 280,665?

 A: 3, 5, 7, 11

Why are those the prime factors of the number 280,665?

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 280,665

280,665
Factor Arrows
393,555
Factor Arrows
331,185
Factor Arrows
310,395
Factor Arrows
33,465
Factor Arrows
31,155
Factor Arrows
3385
Factor Arrows
577
Factor Arrows
711

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:

3, 5, 7, 11

We can check our work by multiplying all of the prime factors together: 3 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 11 = 280,665

This can also be written as 36 x 51 x 71 x 111 = 280,665

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


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