What is the Greatest Common Factor of 12972 and 12982?

Greatest common factor (GCF) of 12972 and 12982 is 2.

GCF(12972,12982) = 2

We will now calculate the prime factors of 12972 and 12982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12972 and 12982.

How to find the GCF of 12972 and 12982?

We will first find the prime factorization of 12972 and 12982. After we will calculate the factors of 12972 and 12982 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 12982

Prime factors of 12982 are 2, 6491. Prime factorization of 12982 in exponential form is:

12982 = 2¹ × 6491¹

Step-3: Factors of 12972

List of positive integer factors of 12972 that divides 12972 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

Step-4: Factors of 12982

List of positive integer factors of 12982 that divides 12972 without a remainder.

1, 2, 6491

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12972 and 12982. The biggest common factor number is the GCF number.
So the greatest common factor 12972 and 12982 is 2.

Also check out the Least Common Multiple of 12972 and 12982