Q: What are the prime factors of the number 123,968?

 A: 2, 13, 149

Why are those the prime factors of the number 123,968?

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 123,968

123,968
Factor Arrows
261,984
Factor Arrows
230,992
Factor Arrows
215,496
Factor Arrows
27,748
Factor Arrows
23,874
Factor Arrows
21,937
Factor Arrows
13149

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, 13, 149

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 13 x 149 = 123,968

This can also be written as 26 x 131 x 1491 = 123,968

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


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