Greatest Common Factor of 1682 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 1682, 1688 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1682 and 1688 is 2.

GCF(1682,1688) = 2

GCF of 1682 and 1688

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

GCF of:
and

Greatest Common Factor of 1682 and 1688

GCF of 1682 and 1688 is 2

Prime Factorization of 1682


2 1682
29 841
29 29
1

Prime factors of 1682 are 2,29. Prime factorization of 1682 in exponential form is:

1682 = 21×292

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 1682 and 1688 is 2

Greatest Common Factor of 1682 and 1688 by matching factors method

Factors of 1682

List of positive integer factors of 1682 that divides 1682 without a remainder.

1,2,29,58,841,1682

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 1682 and 1688. The biggest common factor number is the GCF number.
So the greatest common factor 1682 and 1688 is 2.

Also check out the Least Common Multiple of 1682 and 1688

Properties of GCF 1682 and 1688

(i) The GCF of 1682 and 1688 is associative

GCF of 1682 and 1688 = GCF of 1688 and 1682

Related Greatest Common Factor of 1682

Related Greatest Common Factor of 1688

Frequently Asked Questions on GCF of 1682 and 1688

1. What is the GCF of 1682 and 1688?

Answer: GCF of 1682 and 1688 is 2.

2. What are the Factors of 1682?

Answer: Factors of 1682 are 1, 2, 29, 58, 841, 1682. There are 6 integers that are factors of 1682. The greatest factor of 1682 is 1682.

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 1682 and 1688?

Answer:

Greatest Common Factor of 1682 and 1688 = 2

Step 1: Find the prime factorization of 1682

1682 = 2 x 29 x 29

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

Step 4: Therefore, the greatest common factor of 1682 and 1688 is 2