Q: What are the prime factors of the number 23,272,320?

 A: 2, 3, 5, 17, 23, 31

Why are those the prime factors of the number 23,272,320?

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 23,272,320

23,272,320
Factor Arrows
211,636,160
Factor Arrows
25,818,080
Factor Arrows
22,909,040
Factor Arrows
21,454,520
Factor Arrows
2727,260
Factor Arrows
2363,630
Factor Arrows
2181,815
Factor Arrows
360,605
Factor Arrows
512,121
Factor Arrows
17713
Factor Arrows
2331

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, 5, 17, 23, 31

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 17 x 23 x 31 = 23,272,320

This can also be written as 27 x 31 x 51 x 171 x 231 x 311 = 23,272,320

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


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