What is the Greatest Common Factor of 12954 and 12971?

Greatest common factor (GCF) of 12954 and 12971 is 17.

GCF(12954,12971) = 17

We will now calculate the prime factors of 12954 and 12971, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12954 and 12971.

How to find the GCF of 12954 and 12971?

We will first find the prime factorization of 12954 and 12971. After we will calculate the factors of 12954 and 12971 and find the biggest common factor number .

Step-1: Prime Factorization of 12954

Prime factors of 12954 are 2, 3, 17, 127. Prime factorization of 12954 in exponential form is:

12954 = 2¹ × 3¹ × 17¹ × 127¹

Step-2: 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-3: Factors of 12954

List of positive integer factors of 12954 that divides 12954 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 127, 254, 381, 762, 2159, 4318, 6477

Step-4: Factors of 12971

List of positive integer factors of 12971 that divides 12954 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12954 and 12971. The biggest common factor number is the GCF number.
So the greatest common factor 12954 and 12971 is 17.

Also check out the Least Common Multiple of 12954 and 12971