Greatest Common Factor of 1684 and 1688

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 1684, 1688 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1684 and 1688 is 4.

GCF(1684,1688) = 4

GCF of 1684 and 1688

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

GCF of:
and

Greatest Common Factor of 1684 and 1688

GCF of 1684 and 1688 is 4

Prime Factorization of 1684


2 1684
2 842
421 421
1

Prime factors of 1684 are 2,421. Prime factorization of 1684 in exponential form is:

1684 = 22×4211

Prime Factorization of 1688


2 1688
2 844
2 422
211 211
1

Prime factors of 1688 are 2,211. Prime factorization of 1688 in exponential form is:

1688 = 23×2111

∴ So by taking common prime factors GCF of 1684 and 1688 is 4

Greatest Common Factor of 1684 and 1688 by matching factors method

Factors of 1684

List of positive integer factors of 1684 that divides 1684 without a remainder.

1,2,4,421,842,1684

Factors of 1688

List of positive integer factors of 1688 that divides 1688 without a remainder.

1,2,4,8,211,422,844,1688

Greatest Common Factor

We found the factors and prime factorization of 1684 and 1688. The biggest common factor number is the GCF number.
So the greatest common factor 1684 and 1688 is 4.

Also check out the Least Common Multiple of 1684 and 1688

Properties of GCF 1684 and 1688

(i) The GCF of 1684 and 1688 is associative

GCF of 1684 and 1688 = GCF of 1688 and 1684

Related Greatest Common Factor of 1684

Related Greatest Common Factor of 1688

Frequently Asked Questions on GCF of 1684 and 1688

1. What is the GCF of 1684 and 1688?

Answer: GCF of 1684 and 1688 is 4.

2. What are the Factors of 1684?

Answer: Factors of 1684 are 1, 2, 4, 421, 842, 1684. There are 6 integers that are factors of 1684. The greatest factor of 1684 is 1684.

3. What are the Factors of 1688?

Answer: Factors of 1688 are 1, 2, 4, 8, 211, 422, 844, 1688. There are 8 integers that are factors of 1688. The greatest factor of 1688 is 1688.

4. How to Find the GCF of 1684 and 1688?

Answer:

Greatest Common Factor of 1684 and 1688 = 4

Step 1: Find the prime factorization of 1684

1684 = 2 x 2 x 421

Step 2: Find the prime factorization of 1688

1688 = 2 x 2 x 2 x 211

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 1684 and 1688 is 4