Greatest Common Factor of 176 and 108
GCF(176, 108) = 4, Greatest common factor of 176 and 108 is 4. 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 176 and 108. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 176 and 108 by prime factorization method
We will first find the prime factorization of 176 and 108.
Prime Factorization of 176 is 1, 2, 2, 2, 2, 11 and Prime Factorization of 108 is 1, 2, 2, 3, 3, 3.
- Factorize\( (176) = \) \(1\times 2\times 2\times 2\times 2\times 11\)
- Factorize\( (108) = \) \(1\times 2\times 2\times 3\times 3\times 3\)
Now we need to find any which are common for each number (1, 2, 2) and multiply these numbers together.
\(GCF(176, 108) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 176 and 108 by matching factors method
List of positive integers factors of 176 leaving a remainder zero is 1, 2, 4, 8, 11, 16, 22, 44, 88, 176
List of positive integers factors of 108 leaving a remainder zero is 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
As you can see, 4 is the greatest and common number that 176 and 108 divides into.
So the greatest common factor 176 and 108 is 4.
\(GCF(176, 108) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
