What is the Greatest Common Factor of 6750 and 6770?

Greatest common factor (GCF) of 6750 and 6770 is 10.

GCF(6750,6770) = 10

We will now calculate the prime factors of 6750 and 6770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6750 and 6770.

How to find the GCF of 6750 and 6770?

We will first find the prime factorization of 6750 and 6770. After we will calculate the factors of 6750 and 6770 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 6770

Prime factors of 6770 are 2, 5, 677. Prime factorization of 6770 in exponential form is:

6770 = 2¹ × 5¹ × 677¹

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 6770

List of positive integer factors of 6770 that divides 6750 without a remainder.

1, 2, 5, 10, 677, 1354, 3385

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6750 and 6770. The biggest common factor number is the GCF number.
So the greatest common factor 6750 and 6770 is 10.

Also check out the Least Common Multiple of 6750 and 6770