Greatest Common Factor of 678 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 678, 686 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 678 and 686 is 2.

GCF(678,686) = 2

GCF of 678 and 686

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

GCF of:
and

Greatest Common Factor of 678 and 686

GCF of 678 and 686 is 2

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 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 678 and 686 is 2

Greatest Common Factor of 678 and 686 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 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 678 and 686. The biggest common factor number is the GCF number.
So the greatest common factor 678 and 686 is 2.

Also check out the Least Common Multiple of 678 and 686

Properties of GCF 678 and 686

(i) The GCF of 678 and 686 is associative

GCF of 678 and 686 = GCF of 686 and 678

Related Greatest Common Factor of 678

Related Greatest Common Factor of 686

Frequently Asked Questions on GCF of 678 and 686

1. What is the GCF of 678 and 686?

Answer: GCF of 678 and 686 is 2.

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 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 678 and 686?

Answer:

Greatest Common Factor of 678 and 686 = 2

Step 1: Find the prime factorization of 678

678 = 2 x 3 x 113

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 678 and 686 is 2