Greatest Common Factor of 814 and 822

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 814, 822 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 814 and 822 is 2.

GCF(814,822) = 2

GCF of 814 and 822

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

GCF of:
and

Greatest Common Factor of 814 and 822

GCF of 814 and 822 is 2

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

Prime Factorization of 822


2 822
3 411
137 137
1

Prime factors of 822 are 2,3,137. Prime factorization of 822 in exponential form is:

822 = 21×31×1371

∴ So by taking common prime factors GCF of 814 and 822 is 2

Greatest Common Factor of 814 and 822 by matching factors method

Factors of 814

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

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

Factors of 822

List of positive integer factors of 822 that divides 822 without a remainder.

1,2,3,6,137,274,411,822

Greatest Common Factor

We found the factors and prime factorization of 814 and 822. The biggest common factor number is the GCF number.
So the greatest common factor 814 and 822 is 2.

Also check out the Least Common Multiple of 814 and 822

Properties of GCF 814 and 822

(i) The GCF of 814 and 822 is associative

GCF of 814 and 822 = GCF of 822 and 814

Related Greatest Common Factor of 814

Related Greatest Common Factor of 822

Frequently Asked Questions on GCF of 814 and 822

1. What is the GCF of 814 and 822?

Answer: GCF of 814 and 822 is 2.

2. 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.

3. What are the Factors of 822?

Answer: Factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822. There are 8 integers that are factors of 822. The greatest factor of 822 is 822.

4. How to Find the GCF of 814 and 822?

Answer:

Greatest Common Factor of 814 and 822 = 2

Step 1: Find the prime factorization of 814

814 = 2 x 11 x 37

Step 2: Find the prime factorization of 822

822 = 2 x 3 x 137

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 814 and 822 is 2