Greatest Common Factor of 200 and 2000
GCF(200, 2000) = 200, Greatest common factor of 200 and 2000 is 200. 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 2000. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 200 and 2000 by prime factorization method
We will first find the prime factorization of 200 and 2000.
Prime Factorization of 200 is 1, 2, 2, 2, 5, 5 and Prime Factorization of 2000 is 1, 2, 2, 2, 2, 5, 5, 5.
- Factorize\( (200) = \) \(1\times 2\times 2\times 2\times 5\times 5\)
- Factorize\( (2000) = \) \(1\times 2\times 2\times 2\times 2\times 5\times 5\times 5\)
Now we need to find any which are common for each number (1, 2, 2, 2, 5, 5) and multiply these numbers together.
\(GCF(200, 2000) = 1\times 2\times 2\times 2\times 5\times 5 = 200\).
Greatest Common Factor of 200 and 2000 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 2000 leaving a remainder zero is 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000
As you can see, 200 is the greatest and common number that 200 and 2000 divides into.
So the greatest common factor 200 and 2000 is 200.
\(GCF(200, 2000) = 200\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
