What is the Greatest Common Factor of 12963 and 12972?

Greatest common factor (GCF) of 12963 and 12972 is 3.

GCF(12963,12972) = 3

We will now calculate the prime factors of 12963 and 12972, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12963 and 12972.

How to find the GCF of 12963 and 12972?

We will first find the prime factorization of 12963 and 12972. After we will calculate the factors of 12963 and 12972 and find the biggest common factor number .

Step-1: Prime Factorization of 12963

Prime factors of 12963 are 3, 29, 149. Prime factorization of 12963 in exponential form is:

12963 = 3¹ × 29¹ × 149¹

Step-2: Prime Factorization of 12972

Prime factors of 12972 are 2, 3, 23, 47. Prime factorization of 12972 in exponential form is:

12972 = 2² × 3¹ × 23¹ × 47¹

Step-3: Factors of 12963

List of positive integer factors of 12963 that divides 12963 without a remainder.

1, 3, 29, 87, 149, 447, 4321

Step-4: Factors of 12972

List of positive integer factors of 12972 that divides 12963 without a remainder.

1, 2, 3, 4, 6, 12, 23, 46, 47, 69, 92, 94, 138, 141, 188, 276, 282, 564, 1081, 2162, 3243, 4324, 6486

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12963 and 12972. The biggest common factor number is the GCF number.
So the greatest common factor 12963 and 12972 is 3.

Also check out the Least Common Multiple of 12963 and 12972