Greatest Common Factor of 825 and 828

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 825, 828 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 825 and 828 is 3.

GCF(825,828) = 3

GCF of 825 and 828

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

GCF of:
and

Greatest Common Factor of 825 and 828

GCF of 825 and 828 is 3

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

Prime Factorization of 828


2 828
2 414
3 207
3 69
23 23
1

Prime factors of 828 are 2,3,23. Prime factorization of 828 in exponential form is:

828 = 22×32×231

∴ So by taking common prime factors GCF of 825 and 828 is 3

Greatest Common Factor of 825 and 828 by matching factors method

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

Factors of 828

List of positive integer factors of 828 that divides 828 without a remainder.

1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828

Greatest Common Factor

We found the factors and prime factorization of 825 and 828. The biggest common factor number is the GCF number.
So the greatest common factor 825 and 828 is 3.

Also check out the Least Common Multiple of 825 and 828

Properties of GCF 825 and 828

(i) The GCF of 825 and 828 is associative

GCF of 825 and 828 = GCF of 828 and 825

Related Greatest Common Factor of 825

Related Greatest Common Factor of 828

Frequently Asked Questions on GCF of 825 and 828

1. What is the GCF of 825 and 828?

Answer: GCF of 825 and 828 is 3.

2. 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.

3. What are the Factors of 828?

Answer: Factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828. There are 18 integers that are factors of 828. The greatest factor of 828 is 828.

4. How to Find the GCF of 825 and 828?

Answer:

Greatest Common Factor of 825 and 828 = 3

Step 1: Find the prime factorization of 825

825 = 3 x 5 x 5 x 11

Step 2: Find the prime factorization of 828

828 = 2 x 2 x 3 x 3 x 23

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

GCF = 3

Step 4: Therefore, the greatest common factor of 825 and 828 is 3