Greatest Common Factor of 684 and 688

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

Greatest common factor (GCF) of 684 and 688 is 4.

GCF(684,688) = 4

GCF of 684 and 688

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

GCF of:
and

Greatest Common Factor of 684 and 688

GCF of 684 and 688 is 4

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 688


2 688
2 344
2 172
2 86
43 43
1

Prime factors of 688 are 2,43. Prime factorization of 688 in exponential form is:

688 = 24×431

∴ So by taking common prime factors GCF of 684 and 688 is 4

Greatest Common Factor of 684 and 688 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 688

List of positive integer factors of 688 that divides 688 without a remainder.

1,2,4,8,16,43,86,172,344,688

Greatest Common Factor

We found the factors and prime factorization of 684 and 688. The biggest common factor number is the GCF number.
So the greatest common factor 684 and 688 is 4.

Also check out the Least Common Multiple of 684 and 688

Properties of GCF 684 and 688

(i) The GCF of 684 and 688 is associative

GCF of 684 and 688 = GCF of 688 and 684

Related Greatest Common Factor of 684

Related Greatest Common Factor of 688

Frequently Asked Questions on GCF of 684 and 688

1. What is the GCF of 684 and 688?

Answer: GCF of 684 and 688 is 4.

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 688?

Answer: Factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688. There are 10 integers that are factors of 688. The greatest factor of 688 is 688.

4. How to Find the GCF of 684 and 688?

Answer:

Greatest Common Factor of 684 and 688 = 4

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 688

688 = 2 x 2 x 2 x 2 x 43

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 684 and 688 is 4