Greatest Common Factor of 680 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 680, 686 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 680 and 686 is 2.

GCF(680,686) = 2

GCF of 680 and 686

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

GCF of:
and

Greatest Common Factor of 680 and 686

GCF of 680 and 686 is 2

Prime Factorization of 680


2 680
2 340
2 170
5 85
17 17
1

Prime factors of 680 are 2,5,17. Prime factorization of 680 in exponential form is:

680 = 23×51×171

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 680 and 686 is 2

Greatest Common Factor of 680 and 686 by matching factors method

Factors of 680

List of positive integer factors of 680 that divides 680 without a remainder.

1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680

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 680 and 686. The biggest common factor number is the GCF number.
So the greatest common factor 680 and 686 is 2.

Also check out the Least Common Multiple of 680 and 686

Properties of GCF 680 and 686

(i) The GCF of 680 and 686 is associative

GCF of 680 and 686 = GCF of 686 and 680

Related Greatest Common Factor of 680

Related Greatest Common Factor of 686

Frequently Asked Questions on GCF of 680 and 686

1. What is the GCF of 680 and 686?

Answer: GCF of 680 and 686 is 2.

2. What are the Factors of 680?

Answer: Factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680. There are 16 integers that are factors of 680. The greatest factor of 680 is 680.

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 680 and 686?

Answer:

Greatest Common Factor of 680 and 686 = 2

Step 1: Find the prime factorization of 680

680 = 2 x 2 x 2 x 5 x 17

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 680 and 686 is 2