Greatest Common Factor of 684 and 690

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, 690 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 684 and 690 is 6.

GCF(684,690) = 6

GCF of 684 and 690

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

GCF of:
and

Greatest Common Factor of 684 and 690

GCF of 684 and 690 is 6

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 690


2 690
3 345
5 115
23 23
1

Prime factors of 690 are 2,3,5,23. Prime factorization of 690 in exponential form is:

690 = 21×31×51×231

∴ So by taking common prime factors GCF of 684 and 690 is 6

Greatest Common Factor of 684 and 690 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 690

List of positive integer factors of 690 that divides 690 without a remainder.

1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690

Greatest Common Factor

We found the factors and prime factorization of 684 and 690. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 690 is 6.

Also check out the Least Common Multiple of 684 and 690

Properties of GCF 684 and 690

(i) The GCF of 684 and 690 is associative

GCF of 684 and 690 = GCF of 690 and 684

Related Greatest Common Factor of 684

Related Greatest Common Factor of 690

Frequently Asked Questions on GCF of 684 and 690

1. What is the GCF of 684 and 690?

Answer: GCF of 684 and 690 is 6.

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 690?

Answer: Factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690. There are 16 integers that are factors of 690. The greatest factor of 690 is 690.

4. How to Find the GCF of 684 and 690?

Answer:

Greatest Common Factor of 684 and 690 = 6

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 690

690 = 2 x 3 x 5 x 23

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 684 and 690 is 6