What is the Greatest Common Factor of 12971 and 12985?

Greatest common factor (GCF) of 12971 and 12985 is 7.

GCF(12971,12985) = 7

We will now calculate the prime factors of 12971 and 12985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12971 and 12985.

How to find the GCF of 12971 and 12985?

We will first find the prime factorization of 12971 and 12985. After we will calculate the factors of 12971 and 12985 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 12985

Prime factors of 12985 are 5, 7, 53. Prime factorization of 12985 in exponential form is:

12985 = 5¹ × 7² × 53¹

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 12985

List of positive integer factors of 12985 that divides 12971 without a remainder.

1, 5, 7, 35, 49, 53, 245, 265, 371, 1855, 2597

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12971 and 12985. The biggest common factor number is the GCF number.
So the greatest common factor 12971 and 12985 is 7.

Also check out the Least Common Multiple of 12971 and 12985