What is the Greatest Common Factor of 7742 and 7749?

Greatest common factor (GCF) of 7742 and 7749 is 7.

GCF(7742,7749) = 7

We will now calculate the prime factors of 7742 and 7749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7742 and 7749.

How to find the GCF of 7742 and 7749?

We will first find the prime factorization of 7742 and 7749. After we will calculate the factors of 7742 and 7749 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7749

Prime factors of 7749 are 3, 7, 41. Prime factorization of 7749 in exponential form is:

7749 = 3³ × 7¹ × 41¹

Step-3: Factors of 7742

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

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

Step-4: Factors of 7749

List of positive integer factors of 7749 that divides 7742 without a remainder.

1, 3, 7, 9, 21, 27, 41, 63, 123, 189, 287, 369, 861, 1107, 2583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7742 and 7749. The biggest common factor number is the GCF number.
So the greatest common factor 7742 and 7749 is 7.

Also check out the Least Common Multiple of 7742 and 7749