Q: What are the prime factors of the number 233,103,200?

 A: 2, 5, 11, 26489

Why are those the prime factors of the number 233,103,200?

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 233,103,200

233,103,200
Factor Arrows
2116,551,600
Factor Arrows
258,275,800
Factor Arrows
229,137,900
Factor Arrows
214,568,950
Factor Arrows
27,284,475
Factor Arrows
51,456,895
Factor Arrows
5291,379
Factor Arrows
1126,489

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, 5, 11, 26489

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 2 x 5 x 5 x 11 x 26,489 = 233,103,200

This can also be written as 25 x 52 x 111 x 26,4891 = 233,103,200

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


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