Q: What are the prime factors of the number 11,408?

 A: 2, 23, 31

Why are those the prime factors of the number 11,408?

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 11,408

11,408
Factor Arrows
25,704
Factor Arrows
22,852
Factor Arrows
21,426
Factor Arrows
2713
Factor Arrows
2331

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, 23, 31

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 23 x 31 = 11,408

This can also be written as 24 x 231 x 311 = 11,408

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


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