Greatest Common Factor of 806 and 814

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 806, 814 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 806 and 814 is 2.

GCF(806,814) = 2

GCF of 806 and 814

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

GCF of:
and

Greatest Common Factor of 806 and 814

GCF of 806 and 814 is 2

Prime Factorization of 806


2 806
13 403
31 31
1

Prime factors of 806 are 2,13,31. Prime factorization of 806 in exponential form is:

806 = 21×131×311

Prime Factorization of 814


2 814
11 407
37 37
1

Prime factors of 814 are 2,11,37. Prime factorization of 814 in exponential form is:

814 = 21×111×371

∴ So by taking common prime factors GCF of 806 and 814 is 2

Greatest Common Factor of 806 and 814 by matching factors method

Factors of 806

List of positive integer factors of 806 that divides 806 without a remainder.

1,2,13,26,31,62,403,806

Factors of 814

List of positive integer factors of 814 that divides 814 without a remainder.

1,2,11,22,37,74,407,814

Greatest Common Factor

We found the factors and prime factorization of 806 and 814. The biggest common factor number is the GCF number.
So the greatest common factor 806 and 814 is 2.

Also check out the Least Common Multiple of 806 and 814

Properties of GCF 806 and 814

(i) The GCF of 806 and 814 is associative

GCF of 806 and 814 = GCF of 814 and 806

Related Greatest Common Factor of 806

Related Greatest Common Factor of 814

Frequently Asked Questions on GCF of 806 and 814

1. What is the GCF of 806 and 814?

Answer: GCF of 806 and 814 is 2.

2. What are the Factors of 806?

Answer: Factors of 806 are 1, 2, 13, 26, 31, 62, 403, 806. There are 8 integers that are factors of 806. The greatest factor of 806 is 806.

3. What are the Factors of 814?

Answer: Factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814. There are 8 integers that are factors of 814. The greatest factor of 814 is 814.

4. How to Find the GCF of 806 and 814?

Answer:

Greatest Common Factor of 806 and 814 = 2

Step 1: Find the prime factorization of 806

806 = 2 x 13 x 31

Step 2: Find the prime factorization of 814

814 = 2 x 11 x 37

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 806 and 814 is 2