Greatest Common Factor of 1680 and 1683

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 1680, 1683 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1680 and 1683 is 3.

GCF(1680,1683) = 3

GCF of 1680 and 1683

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

GCF of:
and

Greatest Common Factor of 1680 and 1683

GCF of 1680 and 1683 is 3

Prime Factorization of 1680


2 1680
2 840
2 420
2 210
3 105
5 35
7 7
1

Prime factors of 1680 are 2,3,5,7. Prime factorization of 1680 in exponential form is:

1680 = 24×31×51×71

Prime Factorization of 1683


3 1683
3 561
11 187
17 17
1

Prime factors of 1683 are 3,11,17. Prime factorization of 1683 in exponential form is:

1683 = 32×111×171

∴ So by taking common prime factors GCF of 1680 and 1683 is 3

Greatest Common Factor of 1680 and 1683 by matching factors method

Factors of 1680

List of positive integer factors of 1680 that divides 1680 without a remainder.

1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,35,40,42,48,56,60,70,80,84,105,112,120,140,168,210,240,280,336,420,560,840,1680

Factors of 1683

List of positive integer factors of 1683 that divides 1683 without a remainder.

1,3,9,11,17,33,51,99,153,187,561,1683

Greatest Common Factor

We found the factors and prime factorization of 1680 and 1683. The biggest common factor number is the GCF number.
So the greatest common factor 1680 and 1683 is 3.

Also check out the Least Common Multiple of 1680 and 1683

Properties of GCF 1680 and 1683

(i) The GCF of 1680 and 1683 is associative

GCF of 1680 and 1683 = GCF of 1683 and 1680

Related Greatest Common Factor of 1680

Related Greatest Common Factor of 1683

Frequently Asked Questions on GCF of 1680 and 1683

1. What is the GCF of 1680 and 1683?

Answer: GCF of 1680 and 1683 is 3.

2. What are the Factors of 1680?

Answer: Factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680. There are 40 integers that are factors of 1680. The greatest factor of 1680 is 1680.

3. What are the Factors of 1683?

Answer: Factors of 1683 are 1, 3, 9, 11, 17, 33, 51, 99, 153, 187, 561, 1683. There are 12 integers that are factors of 1683. The greatest factor of 1683 is 1683.

4. How to Find the GCF of 1680 and 1683?

Answer:

Greatest Common Factor of 1680 and 1683 = 3

Step 1: Find the prime factorization of 1680

1680 = 2 x 2 x 2 x 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 1683

1683 = 3 x 3 x 11 x 17

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 1680 and 1683 is 3