Q: What are the prime factors of the number 289,664?

 A: 2, 31, 73

Why are those the prime factors of the number 289,664?

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 289,664

289,664
Factor Arrows
2144,832
Factor Arrows
272,416
Factor Arrows
236,208
Factor Arrows
218,104
Factor Arrows
29,052
Factor Arrows
24,526
Factor Arrows
22,263
Factor Arrows
3173

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, 31, 73

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 2 x 31 x 73 = 289,664

This can also be written as 27 x 311 x 731 = 289,664

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


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