What is the Greatest Common Factor of 1296 and 1311?

Greatest common factor (GCF) of 1296 and 1311 is 3.

GCF(1296,1311) = 3

We will now calculate the prime factors of 1296 and 1311, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1296 and 1311.

How to find the GCF of 1296 and 1311?

We will first find the prime factorization of 1296 and 1311. After we will calculate the factors of 1296 and 1311 and find the biggest common factor number .

Step-1: Prime Factorization of 1296

Prime factors of 1296 are 2, 3. Prime factorization of 1296 in exponential form is:

1296 = 2⁴ × 3⁴

Step-2: Prime Factorization of 1311

Prime factors of 1311 are 3, 19, 23. Prime factorization of 1311 in exponential form is:

1311 = 3¹ × 19¹ × 23¹

Step-3: Factors of 1296

List of positive integer factors of 1296 that divides 1296 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 81, 108, 144, 162, 216, 324, 432, 648

Step-4: Factors of 1311

List of positive integer factors of 1311 that divides 1296 without a remainder.

1, 3, 19, 23, 57, 69, 437

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1296 and 1311. The biggest common factor number is the GCF number.
So the greatest common factor 1296 and 1311 is 3.

Also check out the Least Common Multiple of 1296 and 1311