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