What is the Greatest Common Factor of 138 and 154?

Greatest common factor (GCF) of 138 and 154 is 2.

GCF(138,154) = 2

We will now calculate the prime factors of 138 and 154, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 138 and 154.

How to find the GCF of 138 and 154?

We will first find the prime factorization of 138 and 154. After we will calculate the factors of 138 and 154 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 154

Prime factors of 154 are 2, 7, 11. Prime factorization of 154 in exponential form is:

154 = 2¹ × 7¹ × 11¹

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 154

List of positive integer factors of 154 that divides 138 without a remainder.

1, 2, 7, 11, 14, 22, 77

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 138 and 154. The biggest common factor number is the GCF number.
So the greatest common factor 138 and 154 is 2.

Also check out the Least Common Multiple of 138 and 154