Greatest Common Factor of 20 and 742
GCF(20, 742) = 2, Greatest common factor of 20 and 742 is 2. 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 20 and 742. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 20 and 742 by prime factorization method
We will first find the prime factorization of 20 and 742.
Prime Factorization of 20 is 1, 2, 2, 5 and Prime Factorization of 742 is 1, 2, 7, 53.
- Factorize\( (20) = \) \(1\times 2\times 2\times 5\)
- Factorize\( (742) = \) \(1\times 2\times 7\times 53\)
Now we need to find any which are common for each number (1, 2) and multiply these numbers together.
\(GCF(20, 742) = 1\times 2 = 2\).
Greatest Common Factor of 20 and 742 by matching factors method
List of positive integers factors of 20 leaving a remainder zero is 1, 2, 4, 5, 10, 20
List of positive integers factors of 742 leaving a remainder zero is 1, 2, 7, 14, 53, 106, 371, 742
As you can see, 2 is the greatest and common number that 20 and 742 divides into.
So the greatest common factor 20 and 742 is 2.
\(GCF(20, 742) = 2\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
