Greatest Common Factor of 808 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 808, 814 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 808 and 814 is 2.

GCF(808,814) = 2

GCF of 808 and 814

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

GCF of:
and

Greatest Common Factor of 808 and 814

GCF of 808 and 814 is 2

Prime Factorization of 808


2 808
2 404
2 202
101 101
1

Prime factors of 808 are 2,101. Prime factorization of 808 in exponential form is:

808 = 23×1011

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 808 and 814 is 2

Greatest Common Factor of 808 and 814 by matching factors method

Factors of 808

List of positive integer factors of 808 that divides 808 without a remainder.

1,2,4,8,101,202,404,808

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 808 and 814. The biggest common factor number is the GCF number.
So the greatest common factor 808 and 814 is 2.

Also check out the Least Common Multiple of 808 and 814

Properties of GCF 808 and 814

(i) The GCF of 808 and 814 is associative

GCF of 808 and 814 = GCF of 814 and 808

Related Greatest Common Factor of 808

Related Greatest Common Factor of 814

Frequently Asked Questions on GCF of 808 and 814

1. What is the GCF of 808 and 814?

Answer: GCF of 808 and 814 is 2.

2. What are the Factors of 808?

Answer: Factors of 808 are 1, 2, 4, 8, 101, 202, 404, 808. There are 8 integers that are factors of 808. The greatest factor of 808 is 808.

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 808 and 814?

Answer:

Greatest Common Factor of 808 and 814 = 2

Step 1: Find the prime factorization of 808

808 = 2 x 2 x 2 x 101

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 808 and 814 is 2