What is the Greatest Common Factor of 84 and 91?

Greatest common factor (GCF) of 84 and 91 is 7.

GCF(84,91) = 7

We will now calculate the prime factors of 84 and 91, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 84 and 91.

How to find the GCF of 84 and 91?

We will first find the prime factorization of 84 and 91. After we will calculate the factors of 84 and 91 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 91

Prime factors of 91 are 7, 13. Prime factorization of 91 in exponential form is:

91 = 7¹ × 13¹

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 91

List of positive integer factors of 91 that divides 84 without a remainder.

1, 7, 13

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 84 and 91. The biggest common factor number is the GCF number.
So the greatest common factor 84 and 91 is 7.

Also check out the Least Common Multiple of 84 and 91