Q: What are the prime factors of the number 301,222,140?

 A: 2, 3, 5, 59, 85091

Why are those the prime factors of the number 301,222,140?

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 301,222,140

301,222,140
Factor Arrows
2150,611,070
Factor Arrows
275,305,535
Factor Arrows
325,101,845
Factor Arrows
55,020,369
Factor Arrows
5985,091

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, 59, 85091

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 5 x 59 x 85,091 = 301,222,140

This can also be written as 22 x 31 x 51 x 591 x 85,0911 = 301,222,140

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


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