Q: What are the prime factors of the number 431,122,120?

 A: 2, 5, 11, 13, 23, 29, 113

Why are those the prime factors of the number 431,122,120?

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 431,122,120

431,122,120
Factor Arrows
2215,561,060
Factor Arrows
2107,780,530
Factor Arrows
253,890,265
Factor Arrows
510,778,053
Factor Arrows
11979,823
Factor Arrows
1375,371
Factor Arrows
233,277
Factor Arrows
29113

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, 11, 13, 23, 29, 113

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 5 x 11 x 13 x 23 x 29 x 113 = 431,122,120

This can also be written as 23 x 51 x 111 x 131 x 231 x 291 x 1131 = 431,122,120

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


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