What is the Greatest Common Factor of 6825 and 6838?

Greatest common factor (GCF) of 6825 and 6838 is 13.

GCF(6825,6838) = 13

We will now calculate the prime factors of 6825 and 6838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6825 and 6838.

How to find the GCF of 6825 and 6838?

We will first find the prime factorization of 6825 and 6838. After we will calculate the factors of 6825 and 6838 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 6838

Prime factors of 6838 are 2, 13, 263. Prime factorization of 6838 in exponential form is:

6838 = 2¹ × 13¹ × 263¹

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 6838

List of positive integer factors of 6838 that divides 6825 without a remainder.

1, 2, 13, 26, 263, 526, 3419

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6825 and 6838. The biggest common factor number is the GCF number.
So the greatest common factor 6825 and 6838 is 13.

Also check out the Least Common Multiple of 6825 and 6838