What is the Greatest Common Factor of 825 and 829?

Greatest common factor (GCF) of 825 and 829 is 1.

GCF(825,829) = 1

We will now calculate the prime factors of 825 and 829, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 825 and 829.

How to find the GCF of 825 and 829?

We will first find the prime factorization of 825 and 829. After we will calculate the factors of 825 and 829 and find the biggest common factor number .

Step-1: Prime Factorization of 825

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

825 = 3¹ × 5² × 11¹

Step-2: Prime Factorization of 829

Prime factors of 829 are 829. Prime factorization of 829 in exponential form is:

829 = 829¹

Step-3: 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

Step-4: Factors of 829

List of positive integer factors of 829 that divides 825 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 825 and 829. The biggest common factor number is the GCF number.
So the greatest common factor 825 and 829 is 1.

Also check out the Least Common Multiple of 825 and 829