What is the Greatest Common Factor of 1296 and 1309?

Greatest common factor (GCF) of 1296 and 1309 is 1.

GCF(1296,1309) = 1

We will now calculate the prime factors of 1296 and 1309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1296 and 1309.

How to find the GCF of 1296 and 1309?

We will first find the prime factorization of 1296 and 1309. After we will calculate the factors of 1296 and 1309 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 1309

Prime factors of 1309 are 7, 11, 17. Prime factorization of 1309 in exponential form is:

1309 = 7¹ × 11¹ × 17¹

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 1309

List of positive integer factors of 1309 that divides 1296 without a remainder.

1, 7, 11, 17, 77, 119, 187

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1296 and 1309. The biggest common factor number is the GCF number.
So the greatest common factor 1296 and 1309 is 1.

Also check out the Least Common Multiple of 1296 and 1309