What is the Greatest Common Factor of 123 and 135?

Greatest common factor (GCF) of 123 and 135 is 3.

GCF(123,135) = 3

We will now calculate the prime factors of 123 and 135, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 123 and 135.

How to find the GCF of 123 and 135?

We will first find the prime factorization of 123 and 135. After we will calculate the factors of 123 and 135 and find the biggest common factor number .

Step-1: Prime Factorization of 123

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

123 = 3¹ × 41¹

Step-2: Prime Factorization of 135

Prime factors of 135 are 3, 5. Prime factorization of 135 in exponential form is:

135 = 3³ × 5¹

Step-3: Factors of 123

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

1, 3, 41

Step-4: Factors of 135

List of positive integer factors of 135 that divides 123 without a remainder.

1, 3, 5, 9, 15, 27, 45

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 123 and 135. The biggest common factor number is the GCF number.
So the greatest common factor 123 and 135 is 3.

Also check out the Least Common Multiple of 123 and 135