What is the Greatest Common Factor of 7686 and 7700?

Greatest common factor (GCF) of 7686 and 7700 is 14.

GCF(7686,7700) = 14

We will now calculate the prime factors of 7686 and 7700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7686 and 7700.

How to find the GCF of 7686 and 7700?

We will first find the prime factorization of 7686 and 7700. After we will calculate the factors of 7686 and 7700 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 7700

Prime factors of 7700 are 2, 5, 7, 11. Prime factorization of 7700 in exponential form is:

7700 = 2² × 5² × 7¹ × 11¹

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 7700

List of positive integer factors of 7700 that divides 7686 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 25, 28, 35, 44, 50, 55, 70, 77, 100, 110, 140, 154, 175, 220, 275, 308, 350, 385, 550, 700, 770, 1100, 1540, 1925, 3850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7686 and 7700. The biggest common factor number is the GCF number.
So the greatest common factor 7686 and 7700 is 14.

Also check out the Least Common Multiple of 7686 and 7700