Q: What are the prime factors of the number 262,312,128?

 A: 2, 3, 13, 11677

Why are those the prime factors of the number 262,312,128?

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 262,312,128

262,312,128
Factor Arrows
2131,156,064
Factor Arrows
265,578,032
Factor Arrows
232,789,016
Factor Arrows
216,394,508
Factor Arrows
28,197,254
Factor Arrows
24,098,627
Factor Arrows
31,366,209
Factor Arrows
3455,403
Factor Arrows
3151,801
Factor Arrows
1311,677

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, 11677

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 13 x 11,677 = 262,312,128

This can also be written as 26 x 33 x 131 x 11,6771 = 262,312,128

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


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