Q: What are the prime factors of the number 34,524,000?

 A: 2, 3, 5, 7, 137

Why are those the prime factors of the number 34,524,000?

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 34,524,000

34,524,000
Factor Arrows
217,262,000
Factor Arrows
28,631,000
Factor Arrows
24,315,500
Factor Arrows
22,157,750
Factor Arrows
21,078,875
Factor Arrows
3359,625
Factor Arrows
3119,875
Factor Arrows
523,975
Factor Arrows
54,795
Factor Arrows
5959
Factor Arrows
7137

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, 137

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 5 x 5 x 5 x 7 x 137 = 34,524,000

This can also be written as 25 x 32 x 53 x 71 x 1371 = 34,524,000

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


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