Q: What are the prime factors of the number 324,000?

 A: 2, 3, 5

Why are those the prime factors of the number 324,000?

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 324,000

324,000
Factor Arrows
2162,000
Factor Arrows
281,000
Factor Arrows
240,500
Factor Arrows
220,250
Factor Arrows
210,125
Factor Arrows
33,375
Factor Arrows
31,125
Factor Arrows
3375
Factor Arrows
3125
Factor Arrows
525
Factor Arrows
55

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 3 x 3 x 3 x 3 x 5 x 5 x 5 = 324,000

This can also be written as 25 x 34 x 53 = 324,000

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


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