Q: What are the prime factors of the number 3,633,600?

 A: 2, 3, 5, 757

Why are those the prime factors of the number 3,633,600?

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 3,633,600

3,633,600
Factor Arrows
21,816,800
Factor Arrows
2908,400
Factor Arrows
2454,200
Factor Arrows
2227,100
Factor Arrows
2113,550
Factor Arrows
256,775
Factor Arrows
318,925
Factor Arrows
53,785
Factor Arrows
5757

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, 757

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 5 x 5 x 757 = 3,633,600

This can also be written as 26 x 31 x 52 x 7571 = 3,633,600

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


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