Q: What are the prime factors of the number 34,612,256?

 A: 2, 7, 191, 809

Why are those the prime factors of the number 34,612,256?

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 34,612,256

34,612,256
Factor Arrows
217,306,128
Factor Arrows
28,653,064
Factor Arrows
24,326,532
Factor Arrows
22,163,266
Factor Arrows
21,081,633
Factor Arrows
7154,519
Factor Arrows
191809

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, 191, 809

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 191 x 809 = 34,612,256

This can also be written as 25 x 71 x 1911 x 8091 = 34,612,256

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


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