Q: What are the prime factors of the number 77,728?

 A: 2, 7, 347

Why are those the prime factors of the number 77,728?

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 77,728

77,728
Factor Arrows
238,864
Factor Arrows
219,432
Factor Arrows
29,716
Factor Arrows
24,858
Factor Arrows
22,429
Factor Arrows
7347

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, 347

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 7 x 347 = 77,728

This can also be written as 25 x 71 x 3471 = 77,728

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


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