Q: What are the prime factors of the number 458,322,786?

 A: 2, 3, 29, 31, 1049

Why are those the prime factors of the number 458,322,786?

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 458,322,786

458,322,786
Factor Arrows
2229,161,393
Factor Arrows
376,387,131
Factor Arrows
325,462,377
Factor Arrows
38,487,459
Factor Arrows
32,829,153
Factor Arrows
3943,051
Factor Arrows
2932,519
Factor Arrows
311,049

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, 29, 31, 1049

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 3 x 3 x 29 x 31 x 1,049 = 458,322,786

This can also be written as 21 x 35 x 291 x 311 x 1,0491 = 458,322,786

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


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