What is the Greatest Common Factor of 114 and 120?

Greatest common factor (GCF) of 114 and 120 is 6.

GCF(114,120) = 6

We will now calculate the prime factors of 114 and 120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 114 and 120.

How to find the GCF of 114 and 120?

We will first find the prime factorization of 114 and 120. After we will calculate the factors of 114 and 120 and find the biggest common factor number .

Step-1: Prime Factorization of 114

Prime factors of 114 are 2, 3, 19. Prime factorization of 114 in exponential form is:

114 = 2¹ × 3¹ × 19¹

Step-2: 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-3: Factors of 114

List of positive integer factors of 114 that divides 114 without a remainder.

1, 2, 3, 6, 19, 38, 57

Step-4: Factors of 120

List of positive integer factors of 120 that divides 114 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 114 and 120. The biggest common factor number is the GCF number.
So the greatest common factor 114 and 120 is 6.

Also check out the Least Common Multiple of 114 and 120