Greatest Common Factor of 76 and 6144
GCF(76, 6144) = 4, Greatest common factor of 76 and 6144 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 76 and 6144. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 76 and 6144 by prime factorization method
We will first find the prime factorization of 76 and 6144.
Prime Factorization of 76 is 1, 2, 2, 19 and Prime Factorization of 6144 is 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3.
- Factorize\( (76) = \) \(1\times 2\times 2\times 19\)
- Factorize\( (6144) = \) \(1\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\)
Now we need to find any which are common for each number (1, 2, 2) and multiply these numbers together.
\(GCF(76, 6144) = 1\times 2\times 2 = 4\).
Greatest Common Factor of 76 and 6144 by matching factors method
List of positive integers factors of 76 leaving a remainder zero is 1, 2, 4, 19, 38, 76
List of positive integers factors of 6144 leaving a remainder zero is 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 6144
As you can see, 4 is the greatest and common number that 76 and 6144 divides into.
So the greatest common factor 76 and 6144 is 4.
\(GCF(76, 6144) = 4\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
