Greatest Common Factor of 1806 and 1814

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 1806, 1814 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 1806 and 1814 is 2.

GCF(1806,1814) = 2

GCF of 1806 and 1814

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

GCF of:
and

Greatest Common Factor of 1806 and 1814

GCF of 1806 and 1814 is 2

Prime Factorization of 1806


2 1806
3 903
7 301
43 43
1

Prime factors of 1806 are 2,3,7,43. Prime factorization of 1806 in exponential form is:

1806 = 21×31×71×431

Prime Factorization of 1814


2 1814
907 907
1

Prime factors of 1814 are 2,907. Prime factorization of 1814 in exponential form is:

1814 = 21×9071

∴ So by taking common prime factors GCF of 1806 and 1814 is 2

Greatest Common Factor of 1806 and 1814 by matching factors method

Factors of 1806

List of positive integer factors of 1806 that divides 1806 without a remainder.

1,2,3,6,7,14,21,42,43,86,129,258,301,602,903,1806

Factors of 1814

List of positive integer factors of 1814 that divides 1814 without a remainder.

1,2,907,1814

Greatest Common Factor

We found the factors and prime factorization of 1806 and 1814. The biggest common factor number is the GCF number.
So the greatest common factor 1806 and 1814 is 2.

Also check out the Least Common Multiple of 1806 and 1814

Properties of GCF 1806 and 1814

(i) The GCF of 1806 and 1814 is associative

GCF of 1806 and 1814 = GCF of 1814 and 1806

Related Greatest Common Factor of 1806

Related Greatest Common Factor of 1814

Frequently Asked Questions on GCF of 1806 and 1814

1. What is the GCF of 1806 and 1814?

Answer: GCF of 1806 and 1814 is 2.

2. What are the Factors of 1806?

Answer: Factors of 1806 are 1, 2, 3, 6, 7, 14, 21, 42, 43, 86, 129, 258, 301, 602, 903, 1806. There are 16 integers that are factors of 1806. The greatest factor of 1806 is 1806.

3. What are the Factors of 1814?

Answer: Factors of 1814 are 1, 2, 907, 1814. There are 4 integers that are factors of 1814. The greatest factor of 1814 is 1814.

4. How to Find the GCF of 1806 and 1814?

Answer:

Greatest Common Factor of 1806 and 1814 = 2

Step 1: Find the prime factorization of 1806

1806 = 2 x 3 x 7 x 43

Step 2: Find the prime factorization of 1814

1814 = 2 x 907

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 1806 and 1814 is 2