What is the Greatest Common Factor of 114 and 129?

Greatest common factor (GCF) of 114 and 129 is 3.

GCF(114,129) = 3

We will now calculate the prime factors of 114 and 129, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 114 and 129.

How to find the GCF of 114 and 129?

We will first find the prime factorization of 114 and 129. After we will calculate the factors of 114 and 129 and find the biggest common factor number .

Step-1: Prime Factorization of 114

Prime factors of 114 are 2, 3, 19. Prime factorization of 114 in exponential form is:

114 = 2¹ × 3¹ × 19¹

Step-2: Prime Factorization of 129

Prime factors of 129 are 3, 43. Prime factorization of 129 in exponential form is:

129 = 3¹ × 43¹

Step-3: Factors of 114

List of positive integer factors of 114 that divides 114 without a remainder.

1, 2, 3, 6, 19, 38, 57

Step-4: Factors of 129

List of positive integer factors of 129 that divides 114 without a remainder.

1, 3, 43

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 114 and 129. The biggest common factor number is the GCF number.
So the greatest common factor 114 and 129 is 3.

Also check out the Least Common Multiple of 114 and 129