What is the Greatest Common Factor of 7728 and 7734?

Greatest common factor (GCF) of 7728 and 7734 is 6.

GCF(7728,7734) = 6

We will now calculate the prime factors of 7728 and 7734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7728 and 7734.

How to find the GCF of 7728 and 7734?

We will first find the prime factorization of 7728 and 7734. After we will calculate the factors of 7728 and 7734 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 7734

Prime factors of 7734 are 2, 3, 1289. Prime factorization of 7734 in exponential form is:

7734 = 2¹ × 3¹ × 1289¹

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 7734

List of positive integer factors of 7734 that divides 7728 without a remainder.

1, 2, 3, 6, 1289, 2578, 3867

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7728 and 7734. The biggest common factor number is the GCF number.
So the greatest common factor 7728 and 7734 is 6.

Also check out the Least Common Multiple of 7728 and 7734