Q: What are the prime factors of the number 204,214,230?

 A: 2, 3, 5, 11, 29, 2371

Why are those the prime factors of the number 204,214,230?

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 204,214,230

204,214,230
Factor Arrows
2102,107,115
Factor Arrows
334,035,705
Factor Arrows
311,345,235
Factor Arrows
33,781,745
Factor Arrows
5756,349
Factor Arrows
1168,759
Factor Arrows
292,371

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, 11, 29, 2371

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 5 x 11 x 29 x 2,371 = 204,214,230

This can also be written as 21 x 33 x 51 x 111 x 291 x 2,3711 = 204,214,230

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


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