Greatest Common Factor of 684 and 686

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 684, 686 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 684 and 686 is 2.

GCF(684,686) = 2

GCF of 684 and 686

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

GCF of:
and

Greatest Common Factor of 684 and 686

GCF of 684 and 686 is 2

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

Prime Factorization of 686


2 686
7 343
7 49
7 7
1

Prime factors of 686 are 2,7. Prime factorization of 686 in exponential form is:

686 = 21×73

∴ So by taking common prime factors GCF of 684 and 686 is 2

Greatest Common Factor of 684 and 686 by matching factors method

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

Factors of 686

List of positive integer factors of 686 that divides 686 without a remainder.

1,2,7,14,49,98,343,686

Greatest Common Factor

We found the factors and prime factorization of 684 and 686. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 686 is 2.

Also check out the Least Common Multiple of 684 and 686

Properties of GCF 684 and 686

(i) The GCF of 684 and 686 is associative

GCF of 684 and 686 = GCF of 686 and 684

Related Greatest Common Factor of 684

Related Greatest Common Factor of 686

Frequently Asked Questions on GCF of 684 and 686

1. What is the GCF of 684 and 686?

Answer: GCF of 684 and 686 is 2.

2. 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.

3. What are the Factors of 686?

Answer: Factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686. There are 8 integers that are factors of 686. The greatest factor of 686 is 686.

4. How to Find the GCF of 684 and 686?

Answer:

Greatest Common Factor of 684 and 686 = 2

Step 1: Find the prime factorization of 684

684 = 2 x 2 x 3 x 3 x 19

Step 2: Find the prime factorization of 686

686 = 2 x 7 x 7 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 684 and 686 is 2