What is the Greatest Common Factor of 120 and 138?

Greatest common factor (GCF) of 120 and 138 is 6.

GCF(120,138) = 6

We will now calculate the prime factors of 120 and 138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 120 and 138.

How to find the GCF of 120 and 138?

We will first find the prime factorization of 120 and 138. After we will calculate the factors of 120 and 138 and find the biggest common factor number .

Step-1: Prime Factorization of 120

Prime factors of 120 are 2, 3, 5. Prime factorization of 120 in exponential form is:

120 = 2³ × 3¹ × 5¹

Step-2: 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-3: Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

Step-4: Factors of 138

List of positive integer factors of 138 that divides 120 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 120 and 138. The biggest common factor number is the GCF number.
So the greatest common factor 120 and 138 is 6.

Also check out the Least Common Multiple of 120 and 138