Greatest Common Factor of 1678 and 1680

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 1678, 1680 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1678 and 1680 is 2.

GCF(1678,1680) = 2

GCF of 1678 and 1680

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

GCF of:
and

Greatest Common Factor of 1678 and 1680

GCF of 1678 and 1680 is 2

Prime Factorization of 1678


2 1678
839 839
1

Prime factors of 1678 are 2,839. Prime factorization of 1678 in exponential form is:

1678 = 21×8391

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

∴ So by taking common prime factors GCF of 1678 and 1680 is 2

Greatest Common Factor of 1678 and 1680 by matching factors method

Factors of 1678

List of positive integer factors of 1678 that divides 1678 without a remainder.

1,2,839,1678

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

Greatest Common Factor

We found the factors and prime factorization of 1678 and 1680. The biggest common factor number is the GCF number.
So the greatest common factor 1678 and 1680 is 2.

Also check out the Least Common Multiple of 1678 and 1680

Properties of GCF 1678 and 1680

(i) The GCF of 1678 and 1680 is associative

GCF of 1678 and 1680 = GCF of 1680 and 1678

Related Greatest Common Factor of 1678

Related Greatest Common Factor of 1680

Frequently Asked Questions on GCF of 1678 and 1680

1. What is the GCF of 1678 and 1680?

Answer: GCF of 1678 and 1680 is 2.

2. What are the Factors of 1678?

Answer: Factors of 1678 are 1, 2, 839, 1678. There are 4 integers that are factors of 1678. The greatest factor of 1678 is 1678.

3. 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.

4. How to Find the GCF of 1678 and 1680?

Answer:

Greatest Common Factor of 1678 and 1680 = 2

Step 1: Find the prime factorization of 1678

1678 = 2 x 839

Step 2: Find the prime factorization of 1680

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

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 1678 and 1680 is 2