Q: What are the prime factors of the number 103,416?

 A: 2, 3, 31, 139

Why are those the prime factors of the number 103,416?

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 103,416

103,416
Factor Arrows
251,708
Factor Arrows
225,854
Factor Arrows
212,927
Factor Arrows
34,309
Factor Arrows
31139

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, 31, 139

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 31 x 139 = 103,416

This can also be written as 23 x 31 x 311 x 1391 = 103,416

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


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