Q: What are the prime factors of the number 421,526,560?

 A: 2, 5, 7, 13, 17, 131

Why are those the prime factors of the number 421,526,560?

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 421,526,560

421,526,560
Factor Arrows
2210,763,280
Factor Arrows
2105,381,640
Factor Arrows
252,690,820
Factor Arrows
226,345,410
Factor Arrows
213,172,705
Factor Arrows
52,634,541
Factor Arrows
7376,363
Factor Arrows
1328,951
Factor Arrows
132,227
Factor Arrows
17131

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, 17, 131

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 5 x 7 x 13 x 13 x 17 x 131 = 421,526,560

This can also be written as 25 x 51 x 71 x 132 x 171 x 1311 = 421,526,560

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


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