Greatest Common Factor of 676 and 680

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 676, 680 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 676 and 680 is 4.

GCF(676,680) = 4

GCF of 676 and 680

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

GCF of:
and

Greatest Common Factor of 676 and 680

GCF of 676 and 680 is 4

Prime Factorization of 676


2 676
2 338
13 169
13 13
1

Prime factors of 676 are 2,13. Prime factorization of 676 in exponential form is:

676 = 22×132

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

∴ So by taking common prime factors GCF of 676 and 680 is 4

Greatest Common Factor of 676 and 680 by matching factors method

Factors of 676

List of positive integer factors of 676 that divides 676 without a remainder.

1,2,4,13,26,52,169,338,676

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

Greatest Common Factor

We found the factors and prime factorization of 676 and 680. The biggest common factor number is the GCF number.
So the greatest common factor 676 and 680 is 4.

Also check out the Least Common Multiple of 676 and 680

Properties of GCF 676 and 680

(i) The GCF of 676 and 680 is associative

GCF of 676 and 680 = GCF of 680 and 676

Related Greatest Common Factor of 676

Related Greatest Common Factor of 680

Frequently Asked Questions on GCF of 676 and 680

1. What is the GCF of 676 and 680?

Answer: GCF of 676 and 680 is 4.

2. What are the Factors of 676?

Answer: Factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676. There are 9 integers that are factors of 676. The greatest factor of 676 is 676.

3. 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.

4. How to Find the GCF of 676 and 680?

Answer:

Greatest Common Factor of 676 and 680 = 4

Step 1: Find the prime factorization of 676

676 = 2 x 2 x 13 x 13

Step 2: Find the prime factorization of 680

680 = 2 x 2 x 2 x 5 x 17

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 676 and 680 is 4