Q: What are the prime factors of the number 203,133,125?

 A: 5, 13, 23, 1087

Why are those the prime factors of the number 203,133,125?

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 203,133,125

203,133,125
Factor Arrows
540,626,625
Factor Arrows
58,125,325
Factor Arrows
51,625,065
Factor Arrows
5325,013
Factor Arrows
1325,001
Factor Arrows
231,087

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:

5, 13, 23, 1087

We can check our work by multiplying all of the prime factors together: 5 x 5 x 5 x 5 x 13 x 23 x 1,087 = 203,133,125

This can also be written as 54 x 131 x 231 x 1,0871 = 203,133,125

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


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