Greatest Common Factor of 208 and 224
GCF(208, 224) = 16, Greatest common factor of 208 and 224 is 16. 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 208 and 224. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 208 and 224 by prime factorization method
We will first find the prime factorization of 208 and 224.
Prime Factorization of 208 is 1, 2, 2, 2, 2, 13 and Prime Factorization of 224 is 1, 2, 2, 2, 2, 2, 7.
- Factorize\( (208) = \) \(1\times 2\times 2\times 2\times 2\times 13\)
- Factorize\( (224) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 7\)
Now we need to find any which are common for each number (1, 2, 2, 2, 2) and multiply these numbers together.
\(GCF(208, 224) = 1\times 2\times 2\times 2\times 2 = 16\).
Greatest Common Factor of 208 and 224 by matching factors method
List of positive integers factors of 208 leaving a remainder zero is 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
List of positive integers factors of 224 leaving a remainder zero is 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224
As you can see, 16 is the greatest and common number that 208 and 224 divides into.
So the greatest common factor 208 and 224 is 16.
\(GCF(208, 224) = 16\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
