What is the Greatest Common Factor of 7728 and 7744?

Greatest common factor (GCF) of 7728 and 7744 is 16.

GCF(7728,7744) = 16

We will now calculate the prime factors of 7728 and 7744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7728 and 7744.

How to find the GCF of 7728 and 7744?

We will first find the prime factorization of 7728 and 7744. After we will calculate the factors of 7728 and 7744 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 7744

Prime factors of 7744 are 2, 11. Prime factorization of 7744 in exponential form is:

7744 = 2⁶ × 11²

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 7744

List of positive integer factors of 7744 that divides 7728 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 121, 176, 242, 352, 484, 704, 968, 1936, 3872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7728 and 7744. The biggest common factor number is the GCF number.
So the greatest common factor 7728 and 7744 is 16.

Also check out the Least Common Multiple of 7728 and 7744