What is the Greatest Common Factor of 768 and 786?

Greatest common factor (GCF) of 768 and 786 is 6.

GCF(768,786) = 6

We will now calculate the prime factors of 768 and 786, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 768 and 786.

How to find the GCF of 768 and 786?

We will first find the prime factorization of 768 and 786. After we will calculate the factors of 768 and 786 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 786

Prime factors of 786 are 2, 3, 131. Prime factorization of 786 in exponential form is:

786 = 2¹ × 3¹ × 131¹

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 786

List of positive integer factors of 786 that divides 768 without a remainder.

1, 2, 3, 6, 131, 262, 393

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 768 and 786. The biggest common factor number is the GCF number.
So the greatest common factor 768 and 786 is 6.

Also check out the Least Common Multiple of 768 and 786