Q: What are the prime factors of the number 10,266,312?

 A: 2, 3, 7, 53, 1153

Why are those the prime factors of the number 10,266,312?

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 10,266,312

10,266,312
Factor Arrows
25,133,156
Factor Arrows
22,566,578
Factor Arrows
21,283,289
Factor Arrows
3427,763
Factor Arrows
761,109
Factor Arrows
531,153

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, 53, 1153

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 7 x 53 x 1,153 = 10,266,312

This can also be written as 23 x 31 x 71 x 531 x 1,1531 = 10,266,312

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


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