Q: What are the prime factors of the number 410,624?

 A: 2, 401

Why are those the prime factors of the number 410,624?

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 410,624

410,624
Factor Arrows
2205,312
Factor Arrows
2102,656
Factor Arrows
251,328
Factor Arrows
225,664
Factor Arrows
212,832
Factor Arrows
26,416
Factor Arrows
23,208
Factor Arrows
21,604
Factor Arrows
2802
Factor Arrows
2401

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, 401

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 2 x 2 x 2 x 401 = 410,624

This can also be written as 210 x 4011 = 410,624

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


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