Q: What are the prime factors of the number 300,243,510?

 A: 2, 3, 5, 7, 19, 929

Why are those the prime factors of the number 300,243,510?

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 300,243,510

300,243,510
Factor Arrows
2150,121,755
Factor Arrows
350,040,585
Factor Arrows
316,680,195
Factor Arrows
35,560,065
Factor Arrows
31,853,355
Factor Arrows
3617,785
Factor Arrows
5123,557
Factor Arrows
717,651
Factor Arrows
19929

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, 7, 19, 929

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 3 x 3 x 5 x 7 x 19 x 929 = 300,243,510

This can also be written as 21 x 35 x 51 x 71 x 191 x 9291 = 300,243,510

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


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