Q: What are the prime factors of the number 402,896?

 A: 2, 13, 149

Why are those the prime factors of the number 402,896?

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 402,896

402,896
Factor Arrows
2201,448
Factor Arrows
2100,724
Factor Arrows
250,362
Factor Arrows
225,181
Factor Arrows
131,937
Factor Arrows
13149

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, 13, 149

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 13 x 13 x 149 = 402,896

This can also be written as 24 x 132 x 1491 = 402,896

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


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