Q: What are the prime factors of the number 46,592?

 A: 2, 7, 13

Why are those the prime factors of the number 46,592?

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 46,592

46,592
Factor Arrows
223,296
Factor Arrows
211,648
Factor Arrows
25,824
Factor Arrows
22,912
Factor Arrows
21,456
Factor Arrows
2728
Factor Arrows
2364
Factor Arrows
2182
Factor Arrows
291
Factor Arrows
713

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, 7, 13

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 2 x 2 x 2 x 7 x 13 = 46,592

This can also be written as 29 x 71 x 131 = 46,592

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


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