What is the Greatest Common Factor of 825 and 834?

Greatest common factor (GCF) of 825 and 834 is 3.

GCF(825,834) = 3

We will now calculate the prime factors of 825 and 834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 825 and 834.

How to find the GCF of 825 and 834?

We will first find the prime factorization of 825 and 834. After we will calculate the factors of 825 and 834 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 834

Prime factors of 834 are 2, 3, 139. Prime factorization of 834 in exponential form is:

834 = 2¹ × 3¹ × 139¹

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 834

List of positive integer factors of 834 that divides 825 without a remainder.

1, 2, 3, 6, 139, 278, 417

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 825 and 834. The biggest common factor number is the GCF number.
So the greatest common factor 825 and 834 is 3.

Also check out the Least Common Multiple of 825 and 834