What is the Greatest Common Factor of 6735 and 6750?

Greatest common factor (GCF) of 6735 and 6750 is 15.

GCF(6735,6750) = 15

We will now calculate the prime factors of 6735 and 6750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6735 and 6750.

How to find the GCF of 6735 and 6750?

We will first find the prime factorization of 6735 and 6750. After we will calculate the factors of 6735 and 6750 and find the biggest common factor number .

Step-1: Prime Factorization of 6735

Prime factors of 6735 are 3, 5, 449. Prime factorization of 6735 in exponential form is:

6735 = 3¹ × 5¹ × 449¹

Step-2: 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-3: Factors of 6735

List of positive integer factors of 6735 that divides 6735 without a remainder.

1, 3, 5, 15, 449, 1347, 2245

Step-4: Factors of 6750

List of positive integer factors of 6750 that divides 6735 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6735 and 6750. The biggest common factor number is the GCF number.
So the greatest common factor 6735 and 6750 is 15.

Also check out the Least Common Multiple of 6735 and 6750