Q: What are the prime factors of the number 310,408?

 A: 2, 7, 23, 241

Why are those the prime factors of the number 310,408?

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 310,408

310,408
Factor Arrows
2155,204
Factor Arrows
277,602
Factor Arrows
238,801
Factor Arrows
75,543
Factor Arrows
23241

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, 7, 23, 241

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 7 x 23 x 241 = 310,408

This can also be written as 23 x 71 x 231 x 2411 = 310,408

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


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