What is the Greatest Common Factor of 1296 and 1314?

Greatest common factor (GCF) of 1296 and 1314 is 18.

GCF(1296,1314) = 18

We will now calculate the prime factors of 1296 and 1314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1296 and 1314.

How to find the GCF of 1296 and 1314?

We will first find the prime factorization of 1296 and 1314. After we will calculate the factors of 1296 and 1314 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 1314

Prime factors of 1314 are 2, 3, 73. Prime factorization of 1314 in exponential form is:

1314 = 2¹ × 3² × 73¹

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 1314

List of positive integer factors of 1314 that divides 1296 without a remainder.

1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1296 and 1314. The biggest common factor number is the GCF number.
So the greatest common factor 1296 and 1314 is 18.

Also check out the Least Common Multiple of 1296 and 1314