Q: What are the prime factors of the number 303,200,064?

 A: 2, 3, 175463

Why are those the prime factors of the number 303,200,064?

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 303,200,064

303,200,064
Factor Arrows
2151,600,032
Factor Arrows
275,800,016
Factor Arrows
237,900,008
Factor Arrows
218,950,004
Factor Arrows
29,475,002
Factor Arrows
24,737,501
Factor Arrows
31,579,167
Factor Arrows
3526,389
Factor Arrows
3175,463

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, 175463

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 3 x 3 x 3 x 175,463 = 303,200,064

This can also be written as 26 x 33 x 175,4631 = 303,200,064

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


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