What is the Greatest Common Factor of 7734 and 7738?

Greatest common factor (GCF) of 7734 and 7738 is 2.

GCF(7734,7738) = 2

We will now calculate the prime factors of 7734 and 7738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7734 and 7738.

How to find the GCF of 7734 and 7738?

We will first find the prime factorization of 7734 and 7738. After we will calculate the factors of 7734 and 7738 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7738

Prime factors of 7738 are 2, 53, 73. Prime factorization of 7738 in exponential form is:

7738 = 2¹ × 53¹ × 73¹

Step-3: Factors of 7734

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

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

Step-4: Factors of 7738

List of positive integer factors of 7738 that divides 7734 without a remainder.

1, 2, 53, 73, 106, 146, 3869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7734 and 7738. The biggest common factor number is the GCF number.
So the greatest common factor 7734 and 7738 is 2.

Also check out the Least Common Multiple of 7734 and 7738