What is the Greatest Common Factor of 12971 and 12978?

Greatest common factor (GCF) of 12971 and 12978 is 7.

GCF(12971,12978) = 7

We will now calculate the prime factors of 12971 and 12978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12971 and 12978.

How to find the GCF of 12971 and 12978?

We will first find the prime factorization of 12971 and 12978. After we will calculate the factors of 12971 and 12978 and find the biggest common factor number .

Step-1: Prime Factorization of 12971

Prime factors of 12971 are 7, 17, 109. Prime factorization of 12971 in exponential form is:

12971 = 7¹ × 17¹ × 109¹

Step-2: 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-3: Factors of 12971

List of positive integer factors of 12971 that divides 12971 without a remainder.

1, 7, 17, 109, 119, 763, 1853

Step-4: Factors of 12978

List of positive integer factors of 12978 that divides 12971 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12971 and 12978. The biggest common factor number is the GCF number.
So the greatest common factor 12971 and 12978 is 7.

Also check out the Least Common Multiple of 12971 and 12978