Q: What are the prime factors of the number 310,233,300?

 A: 2, 3, 5, 13, 29, 211

Why are those the prime factors of the number 310,233,300?

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 310,233,300

310,233,300
Factor Arrows
2155,116,650
Factor Arrows
277,558,325
Factor Arrows
325,852,775
Factor Arrows
55,170,555
Factor Arrows
51,034,111
Factor Arrows
1379,547
Factor Arrows
136,119
Factor Arrows
29211

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, 13, 29, 211

We can check our work by multiplying all of the prime factors together: 2 x 2 x 3 x 5 x 5 x 13 x 13 x 29 x 211 = 310,233,300

This can also be written as 22 x 31 x 52 x 132 x 291 x 2111 = 310,233,300

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


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