Q: What are the prime factors of the number 105,501,123?

 A: 3, 7, 13, 367

Why are those the prime factors of the number 105,501,123?

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 105,501,123

105,501,123
Factor Arrows
335,167,041
Factor Arrows
311,722,347
Factor Arrows
33,907,449
Factor Arrows
31,302,483
Factor Arrows
3434,161
Factor Arrows
762,023
Factor Arrows
134,771
Factor Arrows
13367

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:

3, 7, 13, 367

We can check our work by multiplying all of the prime factors together: 3 x 3 x 3 x 3 x 3 x 7 x 13 x 13 x 367 = 105,501,123

This can also be written as 35 x 71 x 132 x 3671 = 105,501,123

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


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