Greatest Common Factor of 60 and 78
GCF(60, 78) = 6, Greatest common factor of 60 and 78 is 6. 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 60 and 78. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 60 and 78 by prime factorization method
We will first find the prime factorization of 60 and 78.
Prime Factorization of 60 is 1, 2, 2, 3, 5 and Prime Factorization of 78 is 1, 2, 3, 13.
- Factorize\( (60) = \) \(1\times 2\times 2\times 3\times 5\)
- Factorize\( (78) = \) \(1\times 2\times 3\times 13\)
Now we need to find any which are common for each number (1, 2, 3) and multiply these numbers together.
\(GCF(60, 78) = 1\times 2\times 3 = 6\).
Greatest Common Factor of 60 and 78 by matching factors method
List of positive integers factors of 60 leaving a remainder zero is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
List of positive integers factors of 78 leaving a remainder zero is 1, 2, 3, 6, 13, 26, 39, 78
As you can see, 6 is the greatest and common number that 60 and 78 divides into.
So the greatest common factor 60 and 78 is 6.
\(GCF(60, 78) = 6\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
