What is the Greatest Common Factor of 12978 and 12992?

Greatest common factor (GCF) of 12978 and 12992 is 14.

GCF(12978,12992) = 14

We will now calculate the prime factors of 12978 and 12992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12978 and 12992.

How to find the GCF of 12978 and 12992?

We will first find the prime factorization of 12978 and 12992. After we will calculate the factors of 12978 and 12992 and find the biggest common factor number .

Step-1: Prime Factorization of 12978

Prime factors of 12978 are 2, 3, 7, 103. Prime factorization of 12978 in exponential form is:

12978 = 2¹ × 3² × 7¹ × 103¹

Step-2: Prime Factorization of 12992

Prime factors of 12992 are 2, 7, 29. Prime factorization of 12992 in exponential form is:

12992 = 2⁶ × 7¹ × 29¹

Step-3: Factors of 12978

List of positive integer factors of 12978 that divides 12978 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 103, 126, 206, 309, 618, 721, 927, 1442, 1854, 2163, 4326, 6489

Step-4: Factors of 12992

List of positive integer factors of 12992 that divides 12978 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 29, 32, 56, 58, 64, 112, 116, 203, 224, 232, 406, 448, 464, 812, 928, 1624, 1856, 3248, 6496

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12978 and 12992. The biggest common factor number is the GCF number.
So the greatest common factor 12978 and 12992 is 14.

Also check out the Least Common Multiple of 12978 and 12992