Greatest Common Factor of 64 and 140
GCF(64, 140) = 4, Greatest common factor of 64 and 140 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 64 and 140. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 64 and 140 by prime factorization method
We will first find the prime factorization of 64 and 140.
Prime Factorization of 64 is 1, 2, 2, 2, 2, 2, 2 and Prime Factorization of 140 is 1, 2, 2, 5, 7.
- Factorize\( (64) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\)
- Factorize\( (140) = \) \(1\times 2\times 2\times 5\times 7\)
Now we need to find any which are common for each number (1, 2, 2) and multiply these numbers together.
\(GCF(64, 140) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 64 and 140 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 140 leaving a remainder zero is 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
As you can see, 4 is the greatest and common number that 64 and 140 divides into.
So the greatest common factor 64 and 140 is 4.
\(GCF(64, 140) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
