Q: What are the prime factors of the number 462,214,480?

 A: 2, 5, 7, 13, 173, 367

Why are those the prime factors of the number 462,214,480?

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 462,214,480

462,214,480
Factor Arrows
2231,107,240
Factor Arrows
2115,553,620
Factor Arrows
257,776,810
Factor Arrows
228,888,405
Factor Arrows
55,777,681
Factor Arrows
7825,383
Factor Arrows
1363,491
Factor Arrows
173367

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, 5, 7, 13, 173, 367

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 5 x 7 x 13 x 173 x 367 = 462,214,480

This can also be written as 24 x 51 x 71 x 131 x 1731 x 3671 = 462,214,480

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


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