Greatest Common Factor of 972 and 164
GCF(972, 164) = 4, Greatest common factor of 972 and 164 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 972 and 164. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 972 and 164 by prime factorization method
We will first find the prime factorization of 972 and 164.
Prime Factorization of 972 is 1, 2, 2, 3, 3, 3, 3, 3 and Prime Factorization of 164 is 1, 2, 2, 41.
- Factorize\( (972) = \) \(1\times 2\times 2\times 3\times 3\times 3\times 3\times 3\)
- Factorize\( (164) = \) \(1\times 2\times 2\times 41\)
Now we need to find any which are common for each number (1, 2, 2) and multiply these numbers together.
\(GCF(972, 164) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 972 and 164 by matching factors method
List of positive integers factors of 972 leaving a remainder zero is 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972
List of positive integers factors of 164 leaving a remainder zero is 1, 2, 4, 41, 82, 164
As you can see, 4 is the greatest and common number that 972 and 164 divides into.
So the greatest common factor 972 and 164 is 4.
\(GCF(972, 164) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
