What is the Greatest Common Factor of 7744 and 7748?

Greatest common factor (GCF) of 7744 and 7748 is 4.

GCF(7744,7748) = 4

We will now calculate the prime factors of 7744 and 7748, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7744 and 7748.

How to find the GCF of 7744 and 7748?

We will first find the prime factorization of 7744 and 7748. After we will calculate the factors of 7744 and 7748 and find the biggest common factor number .

Step-1: Prime Factorization of 7744

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

7744 = 2⁶ × 11²

Step-2: Prime Factorization of 7748

Prime factors of 7748 are 2, 13, 149. Prime factorization of 7748 in exponential form is:

7748 = 2² × 13¹ × 149¹

Step-3: Factors of 7744

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

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

Step-4: Factors of 7748

List of positive integer factors of 7748 that divides 7744 without a remainder.

1, 2, 4, 13, 26, 52, 149, 298, 596, 1937, 3874

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7744 and 7748. The biggest common factor number is the GCF number.
So the greatest common factor 7744 and 7748 is 4.

Also check out the Least Common Multiple of 7744 and 7748