What is the Greatest Common Factor of 6732 and 6749?

Greatest common factor (GCF) of 6732 and 6749 is 17.

GCF(6732,6749) = 17

We will now calculate the prime factors of 6732 and 6749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6732 and 6749.

How to find the GCF of 6732 and 6749?

We will first find the prime factorization of 6732 and 6749. After we will calculate the factors of 6732 and 6749 and find the biggest common factor number .

Step-1: Prime Factorization of 6732

Prime factors of 6732 are 2, 3, 11, 17. Prime factorization of 6732 in exponential form is:

6732 = 2² × 3² × 11¹ × 17¹

Step-2: Prime Factorization of 6749

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

6749 = 17¹ × 397¹

Step-3: Factors of 6732

List of positive integer factors of 6732 that divides 6732 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 17, 18, 22, 33, 34, 36, 44, 51, 66, 68, 99, 102, 132, 153, 187, 198, 204, 306, 374, 396, 561, 612, 748, 1122, 1683, 2244, 3366

Step-4: Factors of 6749

List of positive integer factors of 6749 that divides 6732 without a remainder.

1, 17, 397

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6732 and 6749. The biggest common factor number is the GCF number.
So the greatest common factor 6732 and 6749 is 17.

Also check out the Least Common Multiple of 6732 and 6749