Greatest Common Factor of 684 and 687

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, 687 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 684 and 687 is 3.

GCF(684,687) = 3

GCF of 684 and 687

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

GCF of:
and

Greatest Common Factor of 684 and 687

GCF of 684 and 687 is 3

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 687


3 687
229 229
1

Prime factors of 687 are 3,229. Prime factorization of 687 in exponential form is:

687 = 31×2291

∴ So by taking common prime factors GCF of 684 and 687 is 3

Greatest Common Factor of 684 and 687 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 687

List of positive integer factors of 687 that divides 687 without a remainder.

1,3,229,687

Greatest Common Factor

We found the factors and prime factorization of 684 and 687. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 687 is 3.

Also check out the Least Common Multiple of 684 and 687

Properties of GCF 684 and 687

(i) The GCF of 684 and 687 is associative

GCF of 684 and 687 = GCF of 687 and 684

Related Greatest Common Factor of 684

Related Greatest Common Factor of 687

Frequently Asked Questions on GCF of 684 and 687

1. What is the GCF of 684 and 687?

Answer: GCF of 684 and 687 is 3.

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 687?

Answer: Factors of 687 are 1, 3, 229, 687. There are 4 integers that are factors of 687. The greatest factor of 687 is 687.

4. How to Find the GCF of 684 and 687?

Answer:

Greatest Common Factor of 684 and 687 = 3

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 687

687 = 3 x 229

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

GCF = 3

Step 4: Therefore, the greatest common factor of 684 and 687 is 3