What is the Greatest Common Factor of 84 and 120?

Greatest common factor (GCF) of 84 and 120 is 12.

GCF(84,120) = 12

We will now calculate the prime factors of 84 and 120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84 and 120.

How to find the GCF of 84 and 120?

We will first find the prime factorization of 84 and 120. After we will calculate the factors of 84 and 120 and find the biggest common factor number .

Step-1: Prime Factorization of 84

Prime factors of 84 are 2, 3, 7. Prime factorization of 84 in exponential form is:

84 = 2² × 3¹ × 7¹

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 84

List of positive integer factors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42

Step-4: Factors of 120

List of positive integer factors of 120 that divides 84 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 84 and 120. The biggest common factor number is the GCF number.
So the greatest common factor 84 and 120 is 12.

Also check out the Least Common Multiple of 84 and 120