Q: What are the prime factors of the number 233,341,200?

 A: 2, 3, 5, 64817

Why are those the prime factors of the number 233,341,200?

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 233,341,200

233,341,200
Factor Arrows
2116,670,600
Factor Arrows
258,335,300
Factor Arrows
229,167,650
Factor Arrows
214,583,825
Factor Arrows
34,861,275
Factor Arrows
31,620,425
Factor Arrows
5324,085
Factor Arrows
564,817

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, 64817

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 64,817 = 233,341,200

This can also be written as 24 x 32 x 52 x 64,8171 = 233,341,200

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


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