Q: What are the prime factors of the number 100,342,224?

 A: 2, 3, 37, 509

Why are those the prime factors of the number 100,342,224?

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 100,342,224

100,342,224
Factor Arrows
250,171,112
Factor Arrows
225,085,556
Factor Arrows
212,542,778
Factor Arrows
26,271,389
Factor Arrows
32,090,463
Factor Arrows
3696,821
Factor Arrows
3718,833
Factor Arrows
37509

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, 3, 37, 509

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 3 x 37 x 37 x 509 = 100,342,224

This can also be written as 24 x 32 x 372 x 5091 = 100,342,224

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


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