Q: What are the prime factors of the number 729,344?

 A: 2, 7, 11, 37

Why are those the prime factors of the number 729,344?

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 729,344

729,344
Factor Arrows
2364,672
Factor Arrows
2182,336
Factor Arrows
291,168
Factor Arrows
245,584
Factor Arrows
222,792
Factor Arrows
211,396
Factor Arrows
25,698
Factor Arrows
22,849
Factor Arrows
7407
Factor Arrows
1137

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, 11, 37

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 7 x 11 x 37 = 729,344

This can also be written as 28 x 71 x 111 x 371 = 729,344

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


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