What is the Greatest Common Factor of 6750 and 6765?

Greatest common factor (GCF) of 6750 and 6765 is 15.

GCF(6750,6765) = 15

We will now calculate the prime factors of 6750 and 6765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6750 and 6765.

How to find the GCF of 6750 and 6765?

We will first find the prime factorization of 6750 and 6765. After we will calculate the factors of 6750 and 6765 and find the biggest common factor number .

Step-1: Prime Factorization of 6750

Prime factors of 6750 are 2, 3, 5. Prime factorization of 6750 in exponential form is:

6750 = 2¹ × 3³ × 5³

Step-2: Prime Factorization of 6765

Prime factors of 6765 are 3, 5, 11, 41. Prime factorization of 6765 in exponential form is:

6765 = 3¹ × 5¹ × 11¹ × 41¹

Step-3: Factors of 6750

List of positive integer factors of 6750 that divides 6750 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 125, 135, 150, 225, 250, 270, 375, 450, 675, 750, 1125, 1350, 2250, 3375

Step-4: Factors of 6765

List of positive integer factors of 6765 that divides 6750 without a remainder.

1, 3, 5, 11, 15, 33, 41, 55, 123, 165, 205, 451, 615, 1353, 2255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6750 and 6765. The biggest common factor number is the GCF number.
So the greatest common factor 6750 and 6765 is 15.

Also check out the Least Common Multiple of 6750 and 6765