What is the Greatest Common Factor of 7686 and 7696?

Greatest common factor (GCF) of 7686 and 7696 is 2.

GCF(7686,7696) = 2

We will now calculate the prime factors of 7686 and 7696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7686 and 7696.

How to find the GCF of 7686 and 7696?

We will first find the prime factorization of 7686 and 7696. After we will calculate the factors of 7686 and 7696 and find the biggest common factor number .

Step-1: Prime Factorization of 7686

Prime factors of 7686 are 2, 3, 7, 61. Prime factorization of 7686 in exponential form is:

7686 = 2¹ × 3² × 7¹ × 61¹

Step-2: Prime Factorization of 7696

Prime factors of 7696 are 2, 13, 37. Prime factorization of 7696 in exponential form is:

7696 = 2⁴ × 13¹ × 37¹

Step-3: Factors of 7686

List of positive integer factors of 7686 that divides 7686 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 61, 63, 122, 126, 183, 366, 427, 549, 854, 1098, 1281, 2562, 3843

Step-4: Factors of 7696

List of positive integer factors of 7696 that divides 7686 without a remainder.

1, 2, 4, 8, 13, 16, 26, 37, 52, 74, 104, 148, 208, 296, 481, 592, 962, 1924, 3848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7686 and 7696. The biggest common factor number is the GCF number.
So the greatest common factor 7686 and 7696 is 2.

Also check out the Least Common Multiple of 7686 and 7696