What is the Greatest Common Factor of 138 and 153?

Greatest common factor (GCF) of 138 and 153 is 3.

GCF(138,153) = 3

We will now calculate the prime factors of 138 and 153, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 138 and 153.

How to find the GCF of 138 and 153?

We will first find the prime factorization of 138 and 153. After we will calculate the factors of 138 and 153 and find the biggest common factor number .

Step-1: Prime Factorization of 138

Prime factors of 138 are 2, 3, 23. Prime factorization of 138 in exponential form is:

138 = 2¹ × 3¹ × 23¹

Step-2: Prime Factorization of 153

Prime factors of 153 are 3, 17. Prime factorization of 153 in exponential form is:

153 = 3² × 17¹

Step-3: Factors of 138

List of positive integer factors of 138 that divides 138 without a remainder.

1, 2, 3, 6, 23, 46, 69

Step-4: Factors of 153

List of positive integer factors of 153 that divides 138 without a remainder.

1, 3, 9, 17, 51

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 138 and 153. The biggest common factor number is the GCF number.
So the greatest common factor 138 and 153 is 3.

Also check out the Least Common Multiple of 138 and 153