What is the Greatest Common Factor of 7728 and 7746?

Greatest common factor (GCF) of 7728 and 7746 is 6.

GCF(7728,7746) = 6

We will now calculate the prime factors of 7728 and 7746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7728 and 7746.

How to find the GCF of 7728 and 7746?

We will first find the prime factorization of 7728 and 7746. After we will calculate the factors of 7728 and 7746 and find the biggest common factor number .

Step-1: Prime Factorization of 7728

Prime factors of 7728 are 2, 3, 7, 23. Prime factorization of 7728 in exponential form is:

7728 = 2⁴ × 3¹ × 7¹ × 23¹

Step-2: Prime Factorization of 7746

Prime factors of 7746 are 2, 3, 1291. Prime factorization of 7746 in exponential form is:

7746 = 2¹ × 3¹ × 1291¹

Step-3: Factors of 7728

List of positive integer factors of 7728 that divides 7728 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 23, 24, 28, 42, 46, 48, 56, 69, 84, 92, 112, 138, 161, 168, 184, 276, 322, 336, 368, 483, 552, 644, 966, 1104, 1288, 1932, 2576, 3864

Step-4: Factors of 7746

List of positive integer factors of 7746 that divides 7728 without a remainder.

1, 2, 3, 6, 1291, 2582, 3873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7728 and 7746. The biggest common factor number is the GCF number.
So the greatest common factor 7728 and 7746 is 6.

Also check out the Least Common Multiple of 7728 and 7746