Q: What are the prime factors of the number 103,680?

 A: 2, 3, 5

Why are those the prime factors of the number 103,680?

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 103,680

103,680
Factor Arrows
251,840
Factor Arrows
225,920
Factor Arrows
212,960
Factor Arrows
26,480
Factor Arrows
23,240
Factor Arrows
21,620
Factor Arrows
2810
Factor Arrows
2405
Factor Arrows
3135
Factor Arrows
345
Factor Arrows
315
Factor Arrows
35

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

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 3 x 3 x 3 x 3 x 5 = 103,680

This can also be written as 28 x 34 x 51 = 103,680

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


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