Q: What are the prime factors of the number 204,406,500?

 A: 2, 3, 5, 29, 37, 127

Why are those the prime factors of the number 204,406,500?

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 204,406,500

204,406,500
Factor Arrows
2102,203,250
Factor Arrows
251,101,625
Factor Arrows
317,033,875
Factor Arrows
53,406,775
Factor Arrows
5681,355
Factor Arrows
5136,271
Factor Arrows
294,699
Factor Arrows
37127

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, 3, 5, 29, 37, 127

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 5 x 5 x 5 x 29 x 37 x 127 = 204,406,500

This can also be written as 22 x 31 x 53 x 291 x 371 x 1271 = 204,406,500

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


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