Q: What are the prime factors of the number 51,480?

 A: 2, 3, 5, 11, 13

Why are those the prime factors of the number 51,480?

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 51,480

51,480
Factor Arrows
225,740
Factor Arrows
212,870
Factor Arrows
26,435
Factor Arrows
32,145
Factor Arrows
3715
Factor Arrows
5143
Factor Arrows
1113

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, 11, 13

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 3 x 3 x 5 x 11 x 13 = 51,480

This can also be written as 23 x 32 x 51 x 111 x 131 = 51,480

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


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