Q: What are the prime factors of the number 108,800?

 A: 2, 5, 17

Why are those the prime factors of the number 108,800?

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 108,800

108,800
Factor Arrows
254,400
Factor Arrows
227,200
Factor Arrows
213,600
Factor Arrows
26,800
Factor Arrows
23,400
Factor Arrows
21,700
Factor Arrows
2850
Factor Arrows
2425
Factor Arrows
585
Factor Arrows
517

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, 5, 17

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 2 x 5 x 5 x 17 = 108,800

This can also be written as 28 x 52 x 171 = 108,800

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


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