Q: What are the prime factors of the number 305,404,020?

 A: 2, 3, 5, 53, 3557

Why are those the prime factors of the number 305,404,020?

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 305,404,020

305,404,020
Factor Arrows
2152,702,010
Factor Arrows
276,351,005
Factor Arrows
325,450,335
Factor Arrows
38,483,445
Factor Arrows
32,827,815
Factor Arrows
3942,605
Factor Arrows
5188,521
Factor Arrows
533,557

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, 53, 3557

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 3 x 3 x 3 x 5 x 53 x 3,557 = 305,404,020

This can also be written as 22 x 34 x 51 x 531 x 3,5571 = 305,404,020

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


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