Q: What are the prime factors of the number 335,405,304?

 A: 2, 3, 13, 293, 1223

Why are those the prime factors of the number 335,405,304?

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 335,405,304

335,405,304
Factor Arrows
2167,702,652
Factor Arrows
283,851,326
Factor Arrows
241,925,663
Factor Arrows
313,975,221
Factor Arrows
34,658,407
Factor Arrows
13358,339
Factor Arrows
2931,223

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, 13, 293, 1223

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 13 x 293 x 1,223 = 335,405,304

This can also be written as 23 x 32 x 131 x 2931 x 1,2231 = 335,405,304

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


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