What is the Greatest Common Factor of 656 and 676?

Greatest common factor (GCF) of 656 and 676 is 4.

GCF(656,676) = 4

We will now calculate the prime factors of 656 and 676, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 656 and 676.

How to find the GCF of 656 and 676?

We will first find the prime factorization of 656 and 676. After we will calculate the factors of 656 and 676 and find the biggest common factor number .

Step-1: Prime Factorization of 656

Prime factors of 656 are 2, 41. Prime factorization of 656 in exponential form is:

656 = 2⁴ × 41¹

Step-2: Prime Factorization of 676

Prime factors of 676 are 2, 13. Prime factorization of 676 in exponential form is:

676 = 2² × 13²

Step-3: Factors of 656

List of positive integer factors of 656 that divides 656 without a remainder.

1, 2, 4, 8, 16, 41, 82, 164, 328

Step-4: Factors of 676

List of positive integer factors of 676 that divides 656 without a remainder.

1, 2, 4, 13, 26, 52, 169, 338

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 656 and 676. The biggest common factor number is the GCF number.
So the greatest common factor 656 and 676 is 4.

Also check out the Least Common Multiple of 656 and 676