What is the Greatest Common Factor of 6814 and 6825?

Greatest common factor (GCF) of 6814 and 6825 is 1.

GCF(6814,6825) = 1

We will now calculate the prime factors of 6814 and 6825, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6814 and 6825.

How to find the GCF of 6814 and 6825?

We will first find the prime factorization of 6814 and 6825. After we will calculate the factors of 6814 and 6825 and find the biggest common factor number .

Step-1: Prime Factorization of 6814

Prime factors of 6814 are 2, 3407. Prime factorization of 6814 in exponential form is:

6814 = 2¹ × 3407¹

Step-2: 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-3: Factors of 6814

List of positive integer factors of 6814 that divides 6814 without a remainder.

1, 2, 3407

Step-4: Factors of 6825

List of positive integer factors of 6825 that divides 6814 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6814 and 6825. The biggest common factor number is the GCF number.
So the greatest common factor 6814 and 6825 is 1.

Also check out the Least Common Multiple of 6814 and 6825