Q: What are the prime factors of the number 230,301,144?

 A: 2, 3, 131, 2713

Why are those the prime factors of the number 230,301,144?

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 230,301,144

230,301,144
Factor Arrows
2115,150,572
Factor Arrows
257,575,286
Factor Arrows
228,787,643
Factor Arrows
39,595,881
Factor Arrows
33,198,627
Factor Arrows
31,066,209
Factor Arrows
3355,403
Factor Arrows
1312,713

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, 131, 2713

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 3 x 3 x 131 x 2,713 = 230,301,144

This can also be written as 23 x 34 x 1311 x 2,7131 = 230,301,144

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


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