Greatest Common Factor of 820 and 825

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 820, 825 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 820 and 825 is 5.

GCF(820,825) = 5

GCF of 820 and 825

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

GCF of:
and

Greatest Common Factor of 820 and 825

GCF of 820 and 825 is 5

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

Prime Factorization of 825


3 825
5 275
5 55
11 11
1

Prime factors of 825 are 3,5,11. Prime factorization of 825 in exponential form is:

825 = 31×52×111

∴ So by taking common prime factors GCF of 820 and 825 is 5

Greatest Common Factor of 820 and 825 by matching factors method

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

Factors of 825

List of positive integer factors of 825 that divides 825 without a remainder.

1,3,5,11,15,25,33,55,75,165,275,825

Greatest Common Factor

We found the factors and prime factorization of 820 and 825. The biggest common factor number is the GCF number.
So the greatest common factor 820 and 825 is 5.

Also check out the Least Common Multiple of 820 and 825

Properties of GCF 820 and 825

(i) The GCF of 820 and 825 is associative

GCF of 820 and 825 = GCF of 825 and 820

Related Greatest Common Factor of 820

Related Greatest Common Factor of 825

Frequently Asked Questions on GCF of 820 and 825

1. What is the GCF of 820 and 825?

Answer: GCF of 820 and 825 is 5.

2. 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.

3. What are the Factors of 825?

Answer: Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825. There are 12 integers that are factors of 825. The greatest factor of 825 is 825.

4. How to Find the GCF of 820 and 825?

Answer:

Greatest Common Factor of 820 and 825 = 5

Step 1: Find the prime factorization of 820

820 = 2 x 2 x 5 x 41

Step 2: Find the prime factorization of 825

825 = 3 x 5 x 5 x 11

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 5

Step 4: Therefore, the greatest common factor of 820 and 825 is 5