Greatest Common Factor of 678 and 684

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 678, 684 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 678 and 684 is 6.

GCF(678,684) = 6

GCF of 678 and 684

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

GCF of:
and

Greatest Common Factor of 678 and 684

GCF of 678 and 684 is 6

Prime Factorization of 678


2 678
3 339
113 113
1

Prime factors of 678 are 2,3,113. Prime factorization of 678 in exponential form is:

678 = 21×31×1131

Prime Factorization of 684


2 684
2 342
3 171
3 57
19 19
1

Prime factors of 684 are 2,3,19. Prime factorization of 684 in exponential form is:

684 = 22×32×191

∴ So by taking common prime factors GCF of 678 and 684 is 6

Greatest Common Factor of 678 and 684 by matching factors method

Factors of 678

List of positive integer factors of 678 that divides 678 without a remainder.

1,2,3,6,113,226,339,678

Factors of 684

List of positive integer factors of 684 that divides 684 without a remainder.

1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684

Greatest Common Factor

We found the factors and prime factorization of 678 and 684. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 684 is 6.

Also check out the Least Common Multiple of 678 and 684

Properties of GCF 678 and 684

(i) The GCF of 678 and 684 is associative

GCF of 678 and 684 = GCF of 684 and 678

Related Greatest Common Factor of 678

Related Greatest Common Factor of 684

Frequently Asked Questions on GCF of 678 and 684

1. What is the GCF of 678 and 684?

Answer: GCF of 678 and 684 is 6.

2. What are the Factors of 678?

Answer: Factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678. There are 8 integers that are factors of 678. The greatest factor of 678 is 678.

3. What are the Factors of 684?

Answer: Factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684. There are 18 integers that are factors of 684. The greatest factor of 684 is 684.

4. How to Find the GCF of 678 and 684?

Answer:

Greatest Common Factor of 678 and 684 = 6

Step 1: Find the prime factorization of 678

678 = 2 x 3 x 113

Step 2: Find the prime factorization of 684

684 = 2 x 2 x 3 x 3 x 19

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 678 and 684 is 6