Greatest Common Factor of 64 and 72
GCF(64, 72) = 8, Greatest common factor of 64 and 72 is 8. 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 64 and 72. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 64 and 72 by prime factorization method
We will first find the prime factorization of 64 and 72.
Prime Factorization of 64 is 1, 2, 2, 2, 2, 2, 2 and Prime Factorization of 72 is 1, 2, 2, 2, 3, 3.
- Factorize\( (64) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\)
- Factorize\( (72) = \) \(1\times 2\times 2\times 2\times 3\times 3\)
Now we need to find any which are common for each number (1, 2, 2, 2) and multiply these numbers together.
\(GCF(64, 72) = 1\times 2\times 2\times 2 = 8\).
Greatest Common Factor of 64 and 72 by matching factors method
List of positive integers factors of 64 leaving a remainder zero is 1, 2, 4, 8, 16, 32, 64
List of positive integers factors of 72 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
As you can see, 8 is the greatest and common number that 64 and 72 divides into.
So the greatest common factor 64 and 72 is 8.
\(GCF(64, 72) = 8\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
