Q: What are the prime factors of the number 255,200?

 A: 2, 5, 11, 29

Why are those the prime factors of the number 255,200?

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 255,200

255,200
Factor Arrows
2127,600
Factor Arrows
263,800
Factor Arrows
231,900
Factor Arrows
215,950
Factor Arrows
27,975
Factor Arrows
51,595
Factor Arrows
5319
Factor Arrows
1129

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, 29

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 29 = 255,200

This can also be written as 25 x 52 x 111 x 291 = 255,200

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


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