Q: What are the prime factors of the number 303,414,320?

 A: 2, 5, 11, 173, 1993

Why are those the prime factors of the number 303,414,320?

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 303,414,320

303,414,320
Factor Arrows
2151,707,160
Factor Arrows
275,853,580
Factor Arrows
237,926,790
Factor Arrows
218,963,395
Factor Arrows
53,792,679
Factor Arrows
11344,789
Factor Arrows
1731,993

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, 173, 1993

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 5 x 11 x 173 x 1,993 = 303,414,320

This can also be written as 24 x 51 x 111 x 1731 x 1,9931 = 303,414,320

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


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