Q: What are the prime factors of the number 504,000?

 A: 2, 3, 5, 7

Why are those the prime factors of the number 504,000?

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 504,000

504,000
Factor Arrows
2252,000
Factor Arrows
2126,000
Factor Arrows
263,000
Factor Arrows
231,500
Factor Arrows
215,750
Factor Arrows
27,875
Factor Arrows
32,625
Factor Arrows
3875
Factor Arrows
5175
Factor Arrows
535
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 3 x 3 x 5 x 5 x 5 x 7 = 504,000

This can also be written as 26 x 32 x 53 x 71 = 504,000

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


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