Q: What are the prime factors of the number 213,233,200?

 A: 2, 5, 19, 28057

Why are those the prime factors of the number 213,233,200?

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 213,233,200

213,233,200
Factor Arrows
2106,616,600
Factor Arrows
253,308,300
Factor Arrows
226,654,150
Factor Arrows
213,327,075
Factor Arrows
52,665,415
Factor Arrows
5533,083
Factor Arrows
1928,057

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, 19, 28057

We can check our work by multiplying all of the prime factors together: 2 x 2 x 2 x 2 x 5 x 5 x 19 x 28,057 = 213,233,200

This can also be written as 24 x 52 x 191 x 28,0571 = 213,233,200

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


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