Q: What are the prime factors of the number 300,960?

 A: 2, 3, 5, 11, 19

Why are those the prime factors of the number 300,960?

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 300,960

300,960
Factor Arrows
2150,480
Factor Arrows
275,240
Factor Arrows
237,620
Factor Arrows
218,810
Factor Arrows
29,405
Factor Arrows
33,135
Factor Arrows
31,045
Factor Arrows
5209
Factor Arrows
1119

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, 19

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 11 x 19 = 300,960

This can also be written as 25 x 32 x 51 x 111 x 191 = 300,960

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


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