Greatest Common Factor of 200 and 7100
GCF(200, 7100) = 100, Greatest common factor of 200 and 7100 is 100. Greatest Common Factor or Greatest Common Divisor of two numbers is the largest integer by which both the numbers can be divided. There are two different methods to calculate Greatest Common Factor of 200 and 7100. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 200 and 7100 by prime factorization method
We will first find the prime factorization of 200 and 7100.
Prime Factorization of 200 is 1, 2, 2, 2, 5, 5 and Prime Factorization of 7100 is 1, 2, 2, 5, 5, 71.
- Factorize\( (200) = \) \(1\times 2\times 2\times 2\times 5\times 5\)
- Factorize\( (7100) = \) \(1\times 2\times 2\times 5\times 5\times 71\)
Now we need to find any which are common for each number (1, 2, 2, 5, 5) and multiply these numbers together.
\(GCF(200, 7100) = 1\times 2\times 2\times 5\times 5 = 100\).
Greatest Common Factor of 200 and 7100 by matching factors method
List of positive integers factors of 200 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
List of positive integers factors of 7100 leaving a remainder zero is 1, 2, 4, 5, 10, 20, 25, 50, 71, 100, 142, 284, 355, 710, 1420, 1775, 3550, 7100
As you can see, 100 is the greatest and common number that 200 and 7100 divides into.
So the greatest common factor 200 and 7100 is 100.
\(GCF(200, 7100) = 100\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
