What is the Greatest Common Factor of 1296 and 1306?

Greatest common factor (GCF) of 1296 and 1306 is 2.

GCF(1296,1306) = 2

We will now calculate the prime factors of 1296 and 1306, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1296 and 1306.

How to find the GCF of 1296 and 1306?

We will first find the prime factorization of 1296 and 1306. After we will calculate the factors of 1296 and 1306 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 1306

Prime factors of 1306 are 2, 653. Prime factorization of 1306 in exponential form is:

1306 = 2¹ × 653¹

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 1306

List of positive integer factors of 1306 that divides 1296 without a remainder.

1, 2, 653

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1296 and 1306. The biggest common factor number is the GCF number.
So the greatest common factor 1296 and 1306 is 2.

Also check out the Least Common Multiple of 1296 and 1306