# Greatest Common Factor of 82 and 84

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 82, 84 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 82 and 84 is 2.

GCF(82,84) = 2

## GCF of 82 and 84

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

GCF of:
and

### Greatest Common Factor of 82 and 84 by Prime factorization method

Prime Factorization of 82

 2 82 41 41 1

Prime factors of 82 are 2,41. Prime factorization of 82 in exponential form is:

82 = 21×411

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

∴ So by taking common prime factors GCF of 82 and 84 is 2

### Greatest Common Factor of 82 and 84 by matching factors method

Factors of 82

List of positive integer factors of 82 that divides 82 without a remainder.

1,2,41,82

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

Greatest Common Factor

We found the factors and prime factorization of 82 and 84. The biggest common factor number is the GCF number.
So the greatest common factor 82 and 84 is 2.

Also check out the Least Common Multiple of 82 and 84

### Properties of GCF 82 and 84

(i) The GCF of 82 and 84 is associative

GCF of 82 and 84 = GCF of 84 and 82

### Frequently Asked Questions on GCF of 82 and 84

1. What is the GCF of 82 and 84?

Answer: GCF of 82 and 84 is 2.

2. What are the Factors of 82?

Answer: Factors of 82 are 1, 2, 41, 82. There are 4 integers that are factors of 82. The greatest factor of 82 is 82.

3. 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.

4. How to Find the GCF of 82 and 84?

Greatest Common Factor of 82 and 84 = 2

Step 1: Find the prime factorization of 82

82 = 2 x 41

Step 2: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

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

GCF = 2

Step 4: Therefore, the greatest common factor of 82 and 84 is 2