Q: What are the prime factors of the number 33,768?

 A: 2, 3, 7, 67

Why are those the prime factors of the number 33,768?

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 33,768

33,768
Factor Arrows
216,884
Factor Arrows
28,442
Factor Arrows
24,221
Factor Arrows
31,407
Factor Arrows
3469
Factor Arrows
767

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, 7, 67

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 7 x 67 = 33,768

This can also be written as 23 x 32 x 71 x 671 = 33,768

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


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