Q: What are the prime factors of the number 10,100,128?

 A: 2, 23, 13723

Why are those the prime factors of the number 10,100,128?

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 10,100,128

10,100,128
Factor Arrows
25,050,064
Factor Arrows
22,525,032
Factor Arrows
21,262,516
Factor Arrows
2631,258
Factor Arrows
2315,629
Factor Arrows
2313,723

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, 23, 13723

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 23 x 13,723 = 10,100,128

This can also be written as 25 x 231 x 13,7231 = 10,100,128

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


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