Q: What are the prime factors of the number 100,120,320?

 A: 2, 3, 5, 2897

Why are those the prime factors of the number 100,120,320?

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 100,120,320

100,120,320
Factor Arrows
250,060,160
Factor Arrows
225,030,080
Factor Arrows
212,515,040
Factor Arrows
26,257,520
Factor Arrows
23,128,760
Factor Arrows
21,564,380
Factor Arrows
2782,190
Factor Arrows
2391,095
Factor Arrows
3130,365
Factor Arrows
343,455
Factor Arrows
314,485
Factor Arrows
52,897

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, 2897

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 2 x 3 x 3 x 3 x 5 x 2,897 = 100,120,320

This can also be written as 28 x 33 x 51 x 2,8971 = 100,120,320

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


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