Greatest Common Factor of 814 and 820

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

Greatest common factor (GCF) of 814 and 820 is 2.

GCF(814,820) = 2

GCF of 814 and 820

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

GCF of:
and

Greatest Common Factor of 814 and 820

GCF of 814 and 820 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 820


2 820
2 410
5 205
41 41
1

Prime factors of 820 are 2,5,41. Prime factorization of 820 in exponential form is:

820 = 22×51×411

∴ So by taking common prime factors GCF of 814 and 820 is 2

Greatest Common Factor of 814 and 820 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 820

List of positive integer factors of 820 that divides 820 without a remainder.

1,2,4,5,10,20,41,82,164,205,410,820

Greatest Common Factor

We found the factors and prime factorization of 814 and 820. The biggest common factor number is the GCF number.
So the greatest common factor 814 and 820 is 2.

Also check out the Least Common Multiple of 814 and 820

Properties of GCF 814 and 820

(i) The GCF of 814 and 820 is associative

GCF of 814 and 820 = GCF of 820 and 814

Related Greatest Common Factor of 814

Related Greatest Common Factor of 820

Frequently Asked Questions on GCF of 814 and 820

1. What is the GCF of 814 and 820?

Answer: GCF of 814 and 820 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 820?

Answer: Factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820. There are 12 integers that are factors of 820. The greatest factor of 820 is 820.

4. How to Find the GCF of 814 and 820?

Answer:

Greatest Common Factor of 814 and 820 = 2

Step 1: Find the prime factorization of 814

814 = 2 x 11 x 37

Step 2: Find the prime factorization of 820

820 = 2 x 2 x 5 x 41

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 820 is 2