Greatest Common Factor of 60 and 216
GCF(60, 216) = 12, Greatest common factor of 60 and 216 is 12. 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 60 and 216. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 60 and 216 by prime factorization method
We will first find the prime factorization of 60 and 216.
Prime Factorization of 60 is 1, 2, 2, 3, 5 and Prime Factorization of 216 is 1, 2, 2, 2, 3, 3, 3.
- Factorize\( (60) = \) \(1\times 2\times 2\times 3\times 5\)
- Factorize\( (216) = \) \(1\times 2\times 2\times 2\times 3\times 3\times 3\)
Now we need to find any which are common for each number (1, 2, 2, 3) and multiply these numbers together.
\(GCF(60, 216) = 1\times 2\times 2\times 3 = 12\).
Greatest Common Factor of 60 and 216 by matching factors method
List of positive integers factors of 60 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
List of positive integers factors of 216 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
As you can see, 12 is the greatest and common number that 60 and 216 divides into.
So the greatest common factor 60 and 216 is 12.
\(GCF(60, 216) = 12\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
