Greatest Common Factor of 364 and 1274
GCF(364, 1274) = 182, Greatest common factor of 364 and 1274 is 182. 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 364 and 1274. Greatest Common Factor by prime factorization method and Greatest Common Factor by matching factors method.
Greatest Common Factor of 364 and 1274 by prime factorization method
We will first find the prime factorization of 364 and 1274.
Prime Factorization of 364 is 1, 2, 2, 7, 13 and Prime Factorization of 1274 is 1, 2, 7, 7, 13.
- Factorize\( (364) = \) \(1\times 2\times 2\times 7\times 13\)
- Factorize\( (1274) = \) \(1\times 2\times 7\times 7\times 13\)
Now we need to find any which are common for each number (1, 2, 7, 13) and multiply these numbers together.
\(GCF(364, 1274) = 1\times 2\times 7\times 13 = 182\).
Greatest Common Factor of 364 and 1274 by matching factors method
List of positive integers factors of 364 leaving a remainder zero is 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182, 364
List of positive integers factors of 1274 leaving a remainder zero is 1, 2, 7, 13, 14, 26, 49, 91, 98, 182, 637, 1274
As you can see, 182 is the greatest and common number that 364 and 1274 divides into.
So the greatest common factor 364 and 1274 is 182.
\(GCF(364, 1274) = 182\).
If you want to learn more about greatest common divisor, take a look at the Wikipedia page.
