Q: What are the prime factors of the number 402,345,632?

 A: 2, 13, 73, 13249

Why are those the prime factors of the number 402,345,632?

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 402,345,632

402,345,632
Factor Arrows
2201,172,816
Factor Arrows
2100,586,408
Factor Arrows
250,293,204
Factor Arrows
225,146,602
Factor Arrows
212,573,301
Factor Arrows
13967,177
Factor Arrows
7313,249

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, 73, 13249

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 13 x 73 x 13,249 = 402,345,632

This can also be written as 25 x 131 x 731 x 13,2491 = 402,345,632

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


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