What is the Greatest Common Factor of 6744 and 6750?

Greatest common factor (GCF) of 6744 and 6750 is 6.

GCF(6744,6750) = 6

We will now calculate the prime factors of 6744 and 6750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6744 and 6750.

How to find the GCF of 6744 and 6750?

We will first find the prime factorization of 6744 and 6750. After we will calculate the factors of 6744 and 6750 and find the biggest common factor number .

Step-1: Prime Factorization of 6744

Prime factors of 6744 are 2, 3, 281. Prime factorization of 6744 in exponential form is:

6744 = 2³ × 3¹ × 281¹

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 6744

List of positive integer factors of 6744 that divides 6744 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 281, 562, 843, 1124, 1686, 2248, 3372

Step-4: Factors of 6750

List of positive integer factors of 6750 that divides 6744 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 6744 and 6750. The biggest common factor number is the GCF number.
So the greatest common factor 6744 and 6750 is 6.

Also check out the Least Common Multiple of 6744 and 6750