What is the Greatest Common Factor of 12971 and 12988?

Greatest common factor (GCF) of 12971 and 12988 is 17.

GCF(12971,12988) = 17

We will now calculate the prime factors of 12971 and 12988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12971 and 12988.

How to find the GCF of 12971 and 12988?

We will first find the prime factorization of 12971 and 12988. After we will calculate the factors of 12971 and 12988 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 12988

Prime factors of 12988 are 2, 17, 191. Prime factorization of 12988 in exponential form is:

12988 = 2² × 17¹ × 191¹

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 12988

List of positive integer factors of 12988 that divides 12971 without a remainder.

1, 2, 4, 17, 34, 68, 191, 382, 764, 3247, 6494

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12971 and 12988. The biggest common factor number is the GCF number.
So the greatest common factor 12971 and 12988 is 17.

Also check out the Least Common Multiple of 12971 and 12988