Q: What are the prime factors of the number 34,368?

 A: 2, 3, 179

Why are those the prime factors of the number 34,368?

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 34,368

34,368
Factor Arrows
217,184
Factor Arrows
28,592
Factor Arrows
24,296
Factor Arrows
22,148
Factor Arrows
21,074
Factor Arrows
2537
Factor Arrows
3179

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, 179

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 179 = 34,368

This can also be written as 26 x 31 x 1791 = 34,368

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


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