What is the Greatest Common Factor of 108 and 123?

Greatest common factor (GCF) of 108 and 123 is 3.

GCF(108,123) = 3

We will now calculate the prime factors of 108 and 123, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 108 and 123.

How to find the GCF of 108 and 123?

We will first find the prime factorization of 108 and 123. After we will calculate the factors of 108 and 123 and find the biggest common factor number .

Step-1: Prime Factorization of 108

Prime factors of 108 are 2, 3. Prime factorization of 108 in exponential form is:

108 = 2² × 3³

Step-2: Prime Factorization of 123

Prime factors of 123 are 3, 41. Prime factorization of 123 in exponential form is:

123 = 3¹ × 41¹

Step-3: Factors of 108

List of positive integer factors of 108 that divides 108 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54

Step-4: Factors of 123

List of positive integer factors of 123 that divides 108 without a remainder.

1, 3, 41

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 108 and 123. The biggest common factor number is the GCF number.
So the greatest common factor 108 and 123 is 3.

Also check out the Least Common Multiple of 108 and 123