What is the Greatest Common Factor of 756 and 768?

Greatest common factor (GCF) of 756 and 768 is 12.

GCF(756,768) = 12

We will now calculate the prime factors of 756 and 768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 756 and 768.

How to find the GCF of 756 and 768?

We will first find the prime factorization of 756 and 768. After we will calculate the factors of 756 and 768 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 768

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

768 = 2⁸ × 3¹

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 768

List of positive integer factors of 768 that divides 756 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 756 and 768. The biggest common factor number is the GCF number.
So the greatest common factor 756 and 768 is 12.

Also check out the Least Common Multiple of 756 and 768