What is the Greatest Common Factor of 768 and 774?

Greatest common factor (GCF) of 768 and 774 is 6.

GCF(768,774) = 6

We will now calculate the prime factors of 768 and 774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 768 and 774.

How to find the GCF of 768 and 774?

We will first find the prime factorization of 768 and 774. After we will calculate the factors of 768 and 774 and find the biggest common factor number .

Step-1: Prime Factorization of 768

Prime factors of 768 are 2, 3. Prime factorization of 768 in exponential form is:

768 = 2⁸ × 3¹

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 768

List of positive integer factors of 768 that divides 768 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384

Step-4: Factors of 774

List of positive integer factors of 774 that divides 768 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 768 and 774. The biggest common factor number is the GCF number.
So the greatest common factor 768 and 774 is 6.

Also check out the Least Common Multiple of 768 and 774