Q: What are the prime factors of the number 33,696?

 A: 2, 3, 13

Why are those the prime factors of the number 33,696?

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 33,696

33,696
Factor Arrows
216,848
Factor Arrows
28,424
Factor Arrows
24,212
Factor Arrows
22,106
Factor Arrows
21,053
Factor Arrows
3351
Factor Arrows
3117
Factor Arrows
339
Factor Arrows
313

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, 13

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 13 = 33,696

This can also be written as 25 x 34 x 131 = 33,696

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


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