Q: What are the prime factors of the number 801,728,136?

 A: 2, 3, 11, 37, 109, 251

Why are those the prime factors of the number 801,728,136?

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 801,728,136

801,728,136
Factor Arrows
2400,864,068
Factor Arrows
2200,432,034
Factor Arrows
2100,216,017
Factor Arrows
333,405,339
Factor Arrows
311,135,113
Factor Arrows
111,012,283
Factor Arrows
3727,359
Factor Arrows
109251

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, 3, 11, 37, 109, 251

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 11 x 37 x 109 x 251 = 801,728,136

This can also be written as 23 x 32 x 111 x 371 x 1091 x 2511 = 801,728,136

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


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