What is the Greatest Common Factor of 7749 and 7764?

Greatest common factor (GCF) of 7749 and 7764 is 3.

GCF(7749,7764) = 3

We will now calculate the prime factors of 7749 and 7764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7749 and 7764.

How to find the GCF of 7749 and 7764?

We will first find the prime factorization of 7749 and 7764. After we will calculate the factors of 7749 and 7764 and find the biggest common factor number .

Step-1: Prime Factorization of 7749

Prime factors of 7749 are 3, 7, 41. Prime factorization of 7749 in exponential form is:

7749 = 3³ × 7¹ × 41¹

Step-2: Prime Factorization of 7764

Prime factors of 7764 are 2, 3, 647. Prime factorization of 7764 in exponential form is:

7764 = 2² × 3¹ × 647¹

Step-3: Factors of 7749

List of positive integer factors of 7749 that divides 7749 without a remainder.

1, 3, 7, 9, 21, 27, 41, 63, 123, 189, 287, 369, 861, 1107, 2583

Step-4: Factors of 7764

List of positive integer factors of 7764 that divides 7749 without a remainder.

1, 2, 3, 4, 6, 12, 647, 1294, 1941, 2588, 3882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7749 and 7764. The biggest common factor number is the GCF number.
So the greatest common factor 7749 and 7764 is 3.

Also check out the Least Common Multiple of 7749 and 7764