Q: What are the prime factors of the number 303,220,314?

 A: 2, 3, 53, 1999

Why are those the prime factors of the number 303,220,314?

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 303,220,314

303,220,314
Factor Arrows
2151,610,157
Factor Arrows
350,536,719
Factor Arrows
316,845,573
Factor Arrows
35,615,191
Factor Arrows
53105,947
Factor Arrows
531,999

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, 53, 1999

We can check our work by multiplying all of the prime factors together: 2 x 3 x 3 x 3 x 53 x 53 x 1,999 = 303,220,314

This can also be written as 21 x 33 x 532 x 1,9991 = 303,220,314

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


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