Q: What are the prime factors of the number 31,648?

 A: 2, 23, 43

Why are those the prime factors of the number 31,648?

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 31,648

31,648
Factor Arrows
215,824
Factor Arrows
27,912
Factor Arrows
23,956
Factor Arrows
21,978
Factor Arrows
2989
Factor Arrows
2343

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, 43

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 23 x 43 = 31,648

This can also be written as 25 x 231 x 431 = 31,648

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


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