Q: What are the prime factors of the number 310,433,214?

 A: 2, 3, 7, 13, 47, 12097

Why are those the prime factors of the number 310,433,214?

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 310,433,214

310,433,214
Factor Arrows
2155,216,607
Factor Arrows
351,738,869
Factor Arrows
77,391,267
Factor Arrows
13568,559
Factor Arrows
4712,097

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, 7, 13, 47, 12097

We can check our work by multiplying all of the prime factors together: 2 x 3 x 7 x 13 x 47 x 12,097 = 310,433,214

This can also be written as 21 x 31 x 71 x 131 x 471 x 12,0971 = 310,433,214

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


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