# Greatest Common Factor of 84 and 91

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 84, 91 i.e. 7 largest integer by which both the numbers can be divided.

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

GCF(84,91) = 7

## GCF of 84 and 91

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

### Greatest Common Factor of 84 and 91 by Prime factorization method

Prime Factorization of 84

 2 84 2 42 3 21 7 7 1

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

84 = 22×31×71

Prime Factorization of 91

 7 91 13 13 1

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

91 = 71×131

∴ So by taking common prime factors GCF of 84 and 91 is 7

### Greatest Common Factor of 84 and 91 by matching factors method

Factors of 84

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

1,2,3,4,6,7,12,14,21,28,42,84

Factors of 91

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

1,7,13,91

Greatest Common Factor

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

### Properties of GCF 84 and 91

(i) The GCF of 84 and 91 is associative

GCF of 84 and 91 = GCF of 91 and 84

### Frequently Asked Questions on GCF of 84 and 91

1. What is the GCF of 84 and 91?

Answer: GCF of 84 and 91 is 7.

2. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

3. What are the Factors of 91?

Answer: Factors of 91 are 1, 7, 13, 91. There are 4 integers that are factors of 91. The greatest factor of 91 is 91.

4. How to Find the GCF of 84 and 91?

Answer:

Greatest Common Factor of 84 and 91 = 7

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 91

91 = 7 x 13

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 7

Step 4: Therefore, the greatest common factor of 84 and 91 is 7