What is the Greatest Common Factor of 1296 and 1300?

Greatest common factor (GCF) of 1296 and 1300 is 4.

GCF(1296,1300) = 4

We will now calculate the prime factors of 1296 and 1300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1296 and 1300.

How to find the GCF of 1296 and 1300?

We will first find the prime factorization of 1296 and 1300. After we will calculate the factors of 1296 and 1300 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 1300

Prime factors of 1300 are 2, 5, 13. Prime factorization of 1300 in exponential form is:

1300 = 2² × 5² × 13¹

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 1300

List of positive integer factors of 1300 that divides 1296 without a remainder.

1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, 650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1296 and 1300. The biggest common factor number is the GCF number.
So the greatest common factor 1296 and 1300 is 4.

Also check out the Least Common Multiple of 1296 and 1300