What is the Greatest Common Factor of 6750 and 6762?

Greatest common factor (GCF) of 6750 and 6762 is 6.

GCF(6750,6762) = 6

We will now calculate the prime factors of 6750 and 6762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6750 and 6762.

How to find the GCF of 6750 and 6762?

We will first find the prime factorization of 6750 and 6762. After we will calculate the factors of 6750 and 6762 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 6762

Prime factors of 6762 are 2, 3, 7, 23. Prime factorization of 6762 in exponential form is:

6762 = 2¹ × 3¹ × 7² × 23¹

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 6762

List of positive integer factors of 6762 that divides 6750 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 49, 69, 98, 138, 147, 161, 294, 322, 483, 966, 1127, 2254, 3381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6750 and 6762. The biggest common factor number is the GCF number.
So the greatest common factor 6750 and 6762 is 6.

Also check out the Least Common Multiple of 6750 and 6762