Greatest Common Factor of 676 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 676, 684 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 676 and 684 is 4.

GCF(676,684) = 4

GCF of 676 and 684

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

GCF of:
and

Greatest Common Factor of 676 and 684

GCF of 676 and 684 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 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 676 and 684 is 4

Greatest Common Factor of 676 and 684 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 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 676 and 684. The biggest common factor number is the GCF number.
So the greatest common factor 676 and 684 is 4.

Also check out the Least Common Multiple of 676 and 684

Properties of GCF 676 and 684

(i) The GCF of 676 and 684 is associative

GCF of 676 and 684 = GCF of 684 and 676

Related Greatest Common Factor of 676

Related Greatest Common Factor of 684

Frequently Asked Questions on GCF of 676 and 684

1. What is the GCF of 676 and 684?

Answer: GCF of 676 and 684 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 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 676 and 684?

Answer:

Greatest Common Factor of 676 and 684 = 4

Step 1: Find the prime factorization of 676

676 = 2 x 2 x 13 x 13

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 2 = 4

Step 4: Therefore, the greatest common factor of 676 and 684 is 4