Q: What are the prime factors of the number 413,205?

 A: 3, 5, 13, 163

Why are those the prime factors of the number 413,205?

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 413,205

413,205
Factor Arrows
3137,735
Factor Arrows
527,547
Factor Arrows
132,119
Factor Arrows
13163

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, 13, 163

We can check our work by multiplying all of the prime factors together: 3 x 5 x 13 x 13 x 163 = 413,205

This can also be written as 31 x 51 x 132 x 1631 = 413,205

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


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