What is the Greatest Common Factor of 6714 and 6732?

Greatest common factor (GCF) of 6714 and 6732 is 18.

GCF(6714,6732) = 18

We will now calculate the prime factors of 6714 and 6732, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6714 and 6732.

How to find the GCF of 6714 and 6732?

We will first find the prime factorization of 6714 and 6732. After we will calculate the factors of 6714 and 6732 and find the biggest common factor number .

Step-1: Prime Factorization of 6714

Prime factors of 6714 are 2, 3, 373. Prime factorization of 6714 in exponential form is:

6714 = 2¹ × 3² × 373¹

Step-2: 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-3: Factors of 6714

List of positive integer factors of 6714 that divides 6714 without a remainder.

1, 2, 3, 6, 9, 18, 373, 746, 1119, 2238, 3357

Step-4: Factors of 6732

List of positive integer factors of 6732 that divides 6714 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6714 and 6732. The biggest common factor number is the GCF number.
So the greatest common factor 6714 and 6732 is 18.

Also check out the Least Common Multiple of 6714 and 6732