What is the Greatest Common Factor of 6749 and 6766?

Greatest common factor (GCF) of 6749 and 6766 is 17.

GCF(6749,6766) = 17

We will now calculate the prime factors of 6749 and 6766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6749 and 6766.

How to find the GCF of 6749 and 6766?

We will first find the prime factorization of 6749 and 6766. After we will calculate the factors of 6749 and 6766 and find the biggest common factor number .

Step-1: Prime Factorization of 6749

Prime factors of 6749 are 17, 397. Prime factorization of 6749 in exponential form is:

6749 = 17¹ × 397¹

Step-2: Prime Factorization of 6766

Prime factors of 6766 are 2, 17, 199. Prime factorization of 6766 in exponential form is:

6766 = 2¹ × 17¹ × 199¹

Step-3: Factors of 6749

List of positive integer factors of 6749 that divides 6749 without a remainder.

1, 17, 397

Step-4: Factors of 6766

List of positive integer factors of 6766 that divides 6749 without a remainder.

1, 2, 17, 34, 199, 398, 3383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6749 and 6766. The biggest common factor number is the GCF number.
So the greatest common factor 6749 and 6766 is 17.

Also check out the Least Common Multiple of 6749 and 6766