Q: What are the prime factors of the number 478,475,448?

 A: 2, 3, 11, 43, 113, 373

Why are those the prime factors of the number 478,475,448?

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 478,475,448

478,475,448
Factor Arrows
2239,237,724
Factor Arrows
2119,618,862
Factor Arrows
259,809,431
Factor Arrows
319,936,477
Factor Arrows
111,812,407
Factor Arrows
4342,149
Factor Arrows
113373

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, 43, 113, 373

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 11 x 43 x 113 x 373 = 478,475,448

This can also be written as 23 x 31 x 111 x 431 x 1131 x 3731 = 478,475,448

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


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