Q: What are the prime factors of the number 300,171,520?

 A: 2, 5, 11, 21319

Why are those the prime factors of the number 300,171,520?

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 300,171,520

300,171,520
Factor Arrows
2150,085,760
Factor Arrows
275,042,880
Factor Arrows
237,521,440
Factor Arrows
218,760,720
Factor Arrows
29,380,360
Factor Arrows
24,690,180
Factor Arrows
22,345,090
Factor Arrows
21,172,545
Factor Arrows
5234,509
Factor Arrows
1121,319

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, 5, 11, 21319

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 11 x 21,319 = 300,171,520

This can also be written as 28 x 51 x 111 x 21,3191 = 300,171,520

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


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