What is the Greatest Common Factor of 7728 and 7742?

Greatest common factor (GCF) of 7728 and 7742 is 14.

GCF(7728,7742) = 14

We will now calculate the prime factors of 7728 and 7742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7728 and 7742.

How to find the GCF of 7728 and 7742?

We will first find the prime factorization of 7728 and 7742. After we will calculate the factors of 7728 and 7742 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 7742

Prime factors of 7742 are 2, 7, 79. Prime factorization of 7742 in exponential form is:

7742 = 2¹ × 7² × 79¹

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 7742

List of positive integer factors of 7742 that divides 7728 without a remainder.

1, 2, 7, 14, 49, 79, 98, 158, 553, 1106, 3871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7728 and 7742. The biggest common factor number is the GCF number.
So the greatest common factor 7728 and 7742 is 14.

Also check out the Least Common Multiple of 7728 and 7742