What is the Greatest Common Factor of 12768 and 12774?

Greatest common factor (GCF) of 12768 and 12774 is 6.

GCF(12768,12774) = 6

We will now calculate the prime factors of 12768 and 12774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12768 and 12774.

How to find the GCF of 12768 and 12774?

We will first find the prime factorization of 12768 and 12774. After we will calculate the factors of 12768 and 12774 and find the biggest common factor number .

Step-1: Prime Factorization of 12768

Prime factors of 12768 are 2, 3, 7, 19. Prime factorization of 12768 in exponential form is:

12768 = 2⁵ × 3¹ × 7¹ × 19¹

Step-2: Prime Factorization of 12774

Prime factors of 12774 are 2, 3, 2129. Prime factorization of 12774 in exponential form is:

12774 = 2¹ × 3¹ × 2129¹

Step-3: Factors of 12768

List of positive integer factors of 12768 that divides 12768 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 19, 21, 24, 28, 32, 38, 42, 48, 56, 57, 76, 84, 96, 112, 114, 133, 152, 168, 224, 228, 266, 304, 336, 399, 456, 532, 608, 672, 798, 912, 1064, 1596, 1824, 2128, 3192, 4256, 6384

Step-4: Factors of 12774

List of positive integer factors of 12774 that divides 12768 without a remainder.

1, 2, 3, 6, 2129, 4258, 6387

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12768 and 12774. The biggest common factor number is the GCF number.
So the greatest common factor 12768 and 12774 is 6.

Also check out the Least Common Multiple of 12768 and 12774