Q: What are the prime factors of the number 123,904?

 A: 2, 11

Why are those the prime factors of the number 123,904?

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 123,904

123,904
Factor Arrows
261,952
Factor Arrows
230,976
Factor Arrows
215,488
Factor Arrows
27,744
Factor Arrows
23,872
Factor Arrows
21,936
Factor Arrows
2968
Factor Arrows
2484
Factor Arrows
2242
Factor Arrows
2121
Factor Arrows
1111

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, 11

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 2 x 2 x 11 x 11 = 123,904

This can also be written as 210 x 112 = 123,904

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


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