What is the Greatest Common Factor of 6825 and 6837?

Greatest common factor (GCF) of 6825 and 6837 is 3.

GCF(6825,6837) = 3

We will now calculate the prime factors of 6825 and 6837, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6825 and 6837.

How to find the GCF of 6825 and 6837?

We will first find the prime factorization of 6825 and 6837. After we will calculate the factors of 6825 and 6837 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 6837

Prime factors of 6837 are 3, 43, 53. Prime factorization of 6837 in exponential form is:

6837 = 3¹ × 43¹ × 53¹

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 6837

List of positive integer factors of 6837 that divides 6825 without a remainder.

1, 3, 43, 53, 129, 159, 2279

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6825 and 6837. The biggest common factor number is the GCF number.
So the greatest common factor 6825 and 6837 is 3.

Also check out the Least Common Multiple of 6825 and 6837