What is the Greatest Common Factor of 138 and 149?

Greatest common factor (GCF) of 138 and 149 is 1.

GCF(138,149) = 1

We will now calculate the prime factors of 138 and 149, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 138 and 149.

How to find the GCF of 138 and 149?

We will first find the prime factorization of 138 and 149. After we will calculate the factors of 138 and 149 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 149

Prime factors of 149 are 149. Prime factorization of 149 in exponential form is:

149 = 149¹

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 149

List of positive integer factors of 149 that divides 138 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 138 and 149. The biggest common factor number is the GCF number.
So the greatest common factor 138 and 149 is 1.

Also check out the Least Common Multiple of 138 and 149