Greatest Common Factor of 78 and 84

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 78, 84 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 78 and 84 is 6.

GCF(78,84) = 6

GCF of 78 and 84

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

GCF of:
and

Greatest Common Factor of 78 and 84

GCF of 78 and 84 is 6

Prime Factorization of 78


2 78
3 39
13 13
1

Prime factors of 78 are 2,3,13. Prime factorization of 78 in exponential form is:

78 = 21×31×131

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 78 and 84 is 6

Greatest Common Factor of 78 and 84 by matching factors method

Factors of 78

List of positive integer factors of 78 that divides 78 without a remainder.

1,2,3,6,13,26,39,78

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 78 and 84. The biggest common factor number is the GCF number.
So the greatest common factor 78 and 84 is 6.

Also check out the Least Common Multiple of 78 and 84

Properties of GCF 78 and 84

(i) The GCF of 78 and 84 is associative

GCF of 78 and 84 = GCF of 84 and 78

Related Greatest Common Factor of 78

Related Greatest Common Factor of 84

Frequently Asked Questions on GCF of 78 and 84

1. What is the GCF of 78 and 84?

Answer: GCF of 78 and 84 is 6.

2. What are the Factors of 78?

Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.

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 78 and 84?

Answer:

Greatest Common Factor of 78 and 84 = 6

Step 1: Find the prime factorization of 78

78 = 2 x 3 x 13

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 x 3 = 6

Step 4: Therefore, the greatest common factor of 78 and 84 is 6