What is the Greatest Common Factor of 756 and 774?

Greatest common factor (GCF) of 756 and 774 is 18.

GCF(756,774) = 18

We will now calculate the prime factors of 756 and 774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 756 and 774.

How to find the GCF of 756 and 774?

We will first find the prime factorization of 756 and 774. After we will calculate the factors of 756 and 774 and find the biggest common factor number .

Step-1: Prime Factorization of 756

Prime factors of 756 are 2, 3, 7. Prime factorization of 756 in exponential form is:

756 = 2² × 3³ × 7¹

Step-2: Prime Factorization of 774

Prime factors of 774 are 2, 3, 43. Prime factorization of 774 in exponential form is:

774 = 2¹ × 3² × 43¹

Step-3: Factors of 756

List of positive integer factors of 756 that divides 756 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 84, 108, 126, 189, 252, 378

Step-4: Factors of 774

List of positive integer factors of 774 that divides 756 without a remainder.

1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 756 and 774. The biggest common factor number is the GCF number.
So the greatest common factor 756 and 774 is 18.

Also check out the Least Common Multiple of 756 and 774