Q: What are the prime factors of the number 753,480?

 A: 2, 3, 5, 7, 13, 23

Why are those the prime factors of the number 753,480?

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 753,480

753,480
Factor Arrows
2376,740
Factor Arrows
2188,370
Factor Arrows
294,185
Factor Arrows
331,395
Factor Arrows
310,465
Factor Arrows
52,093
Factor Arrows
7299
Factor Arrows
1323

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, 13, 23

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 7 x 13 x 23 = 753,480

This can also be written as 23 x 32 x 51 x 71 x 131 x 231 = 753,480

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


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