Q: What are the prime factors of the number 204,002,656?

 A: 2, 11, 13, 109, 409

Why are those the prime factors of the number 204,002,656?

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 204,002,656

204,002,656
Factor Arrows
2102,001,328
Factor Arrows
251,000,664
Factor Arrows
225,500,332
Factor Arrows
212,750,166
Factor Arrows
26,375,083
Factor Arrows
11579,553
Factor Arrows
1344,581
Factor Arrows
109409

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, 11, 13, 109, 409

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 11 x 13 x 109 x 409 = 204,002,656

This can also be written as 25 x 111 x 131 x 1091 x 4091 = 204,002,656

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


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