Greatest Common Factor of 72 and 2208
GCF(72, 2208) = 24, Greatest common factor of 72 and 2208 is 24. 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 2208. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 72 and 2208 by prime factorization method
We will first find the prime factorization of 72 and 2208.
Prime Factorization of 72 is 1, 2, 2, 2, 3, 3 and Prime Factorization of 2208 is 1, 2, 2, 2, 2, 2, 3, 23.
- Factorize\( (72) = \) \(1\times 2\times 2\times 2\times 3\times 3\)
- Factorize\( (2208) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 3\times 23\)
Now we need to find any which are common for each number (1, 2, 2, 2, 3) and multiply these numbers together.
\(GCF(72, 2208) = 1\times 2\times 2\times 2\times 3 = 24\).
Greatest Common Factor of 72 and 2208 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 2208 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104, 2208
As you can see, 24 is the greatest and common number that 72 and 2208 divides into.
So the greatest common factor 72 and 2208 is 24.
\(GCF(72, 2208) = 24\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
