What is the Greatest Common Factor of 768 and 780?

Greatest common factor (GCF) of 768 and 780 is 12.

GCF(768,780) = 12

We will now calculate the prime factors of 768 and 780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 768 and 780.

How to find the GCF of 768 and 780?

We will first find the prime factorization of 768 and 780. After we will calculate the factors of 768 and 780 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 780

Prime factors of 780 are 2, 3, 5, 13. Prime factorization of 780 in exponential form is:

780 = 2² × 3¹ × 5¹ × 13¹

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 780

List of positive integer factors of 780 that divides 768 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 768 and 780. The biggest common factor number is the GCF number.
So the greatest common factor 768 and 780 is 12.

Also check out the Least Common Multiple of 768 and 780