What is the Greatest Common Factor of 84 and 96?

Greatest common factor (GCF) of 84 and 96 is 12.

GCF(84,96) = 12

We will now calculate the prime factors of 84 and 96, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84 and 96.

How to find the GCF of 84 and 96?

We will first find the prime factorization of 84 and 96. After we will calculate the factors of 84 and 96 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 96

Prime factors of 96 are 2, 3. Prime factorization of 96 in exponential form is:

96 = 2⁵ × 3¹

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 96

List of positive integer factors of 96 that divides 84 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84 and 96. The biggest common factor number is the GCF number.
So the greatest common factor 84 and 96 is 12.

Also check out the Least Common Multiple of 84 and 96