Q: What are the prime factors of the number 215,040?

 A: 2, 3, 5, 7

Why are those the prime factors of the number 215,040?

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 215,040

215,040
Factor Arrows
2107,520
Factor Arrows
253,760
Factor Arrows
226,880
Factor Arrows
213,440
Factor Arrows
26,720
Factor Arrows
23,360
Factor Arrows
21,680
Factor Arrows
2840
Factor Arrows
2420
Factor Arrows
2210
Factor Arrows
2105
Factor Arrows
335
Factor Arrows
57

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, 7

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 2 x 2 x 2 x 3 x 5 x 7 = 215,040

This can also be written as 211 x 31 x 51 x 71 = 215,040

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


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