What is the Greatest Common Factor of 7728 and 7740?

Greatest common factor (GCF) of 7728 and 7740 is 12.

GCF(7728,7740) = 12

We will now calculate the prime factors of 7728 and 7740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7728 and 7740.

How to find the GCF of 7728 and 7740?

We will first find the prime factorization of 7728 and 7740. After we will calculate the factors of 7728 and 7740 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 7740

Prime factors of 7740 are 2, 3, 5, 43. Prime factorization of 7740 in exponential form is:

7740 = 2² × 3² × 5¹ × 43¹

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 7740

List of positive integer factors of 7740 that divides 7728 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 43, 45, 60, 86, 90, 129, 172, 180, 215, 258, 387, 430, 516, 645, 774, 860, 1290, 1548, 1935, 2580, 3870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7728 and 7740. The biggest common factor number is the GCF number.
So the greatest common factor 7728 and 7740 is 12.

Also check out the Least Common Multiple of 7728 and 7740