Greatest Common Factor of 200 and 8464
GCF(200, 8464) = 8, Greatest common factor of 200 and 8464 is 8. 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 8464. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 200 and 8464 by prime factorization method
We will first find the prime factorization of 200 and 8464.
Prime Factorization of 200 is 1, 2, 2, 2, 5, 5 and Prime Factorization of 8464 is 1, 2, 2, 2, 2, 23, 23.
- Factorize\( (200) = \) \(1\times 2\times 2\times 2\times 5\times 5\)
- Factorize\( (8464) = \) \(1\times 2\times 2\times 2\times 2\times 23\times 23\)
Now we need to find any which are common for each number (1, 2, 2, 2) and multiply these numbers together.
\(GCF(200, 8464) = 1\times 2\times 2\times 2 = 8\).
Greatest Common Factor of 200 and 8464 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 8464 leaving a remainder zero is 1, 2, 4, 8, 16, 23, 46, 92, 184, 368, 529, 1058, 2116, 4232, 8464
As you can see, 8 is the greatest and common number that 200 and 8464 divides into.
So the greatest common factor 200 and 8464 is 8.
\(GCF(200, 8464) = 8\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
