What is the Greatest Common Factor of 7744 and 7750?

Greatest common factor (GCF) of 7744 and 7750 is 2.

GCF(7744,7750) = 2

We will now calculate the prime factors of 7744 and 7750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7744 and 7750.

How to find the GCF of 7744 and 7750?

We will first find the prime factorization of 7744 and 7750. After we will calculate the factors of 7744 and 7750 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 7750

Prime factors of 7750 are 2, 5, 31. Prime factorization of 7750 in exponential form is:

7750 = 2¹ × 5³ × 31¹

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 7750

List of positive integer factors of 7750 that divides 7744 without a remainder.

1, 2, 5, 10, 25, 31, 50, 62, 125, 155, 250, 310, 775, 1550, 3875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7744 and 7750. The biggest common factor number is the GCF number.
So the greatest common factor 7744 and 7750 is 2.

Also check out the Least Common Multiple of 7744 and 7750