What is the Greatest Common Factor of 6825 and 6834?

Greatest common factor (GCF) of 6825 and 6834 is 3.

GCF(6825,6834) = 3

We will now calculate the prime factors of 6825 and 6834, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6825 and 6834.

How to find the GCF of 6825 and 6834?

We will first find the prime factorization of 6825 and 6834. After we will calculate the factors of 6825 and 6834 and find the biggest common factor number .

Step-1: Prime Factorization of 6825

Prime factors of 6825 are 3, 5, 7, 13. Prime factorization of 6825 in exponential form is:

6825 = 3¹ × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 6834

Prime factors of 6834 are 2, 3, 17, 67. Prime factorization of 6834 in exponential form is:

6834 = 2¹ × 3¹ × 17¹ × 67¹

Step-3: Factors of 6825

List of positive integer factors of 6825 that divides 6825 without a remainder.

1, 3, 5, 7, 13, 15, 21, 25, 35, 39, 65, 75, 91, 105, 175, 195, 273, 325, 455, 525, 975, 1365, 2275

Step-4: Factors of 6834

List of positive integer factors of 6834 that divides 6825 without a remainder.

1, 2, 3, 6, 17, 34, 51, 67, 102, 134, 201, 402, 1139, 2278, 3417

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6825 and 6834. The biggest common factor number is the GCF number.
So the greatest common factor 6825 and 6834 is 3.

Also check out the Least Common Multiple of 6825 and 6834