Q: What are the prime factors of the number 100,310,144?

 A: 2, 11, 191, 373

Why are those the prime factors of the number 100,310,144?

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 100,310,144

100,310,144
Factor Arrows
250,155,072
Factor Arrows
225,077,536
Factor Arrows
212,538,768
Factor Arrows
26,269,384
Factor Arrows
23,134,692
Factor Arrows
21,567,346
Factor Arrows
2783,673
Factor Arrows
1171,243
Factor Arrows
191373

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, 191, 373

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 11 x 191 x 373 = 100,310,144

This can also be written as 27 x 111 x 1911 x 3731 = 100,310,144

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


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