What is the Greatest Common Factor of 7686 and 7704?

Greatest common factor (GCF) of 7686 and 7704 is 18.

GCF(7686,7704) = 18

We will now calculate the prime factors of 7686 and 7704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7686 and 7704.

How to find the GCF of 7686 and 7704?

We will first find the prime factorization of 7686 and 7704. After we will calculate the factors of 7686 and 7704 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 7704

Prime factors of 7704 are 2, 3, 107. Prime factorization of 7704 in exponential form is:

7704 = 2³ × 3² × 107¹

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 7704

List of positive integer factors of 7704 that divides 7686 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 107, 214, 321, 428, 642, 856, 963, 1284, 1926, 2568, 3852

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7686 and 7704. The biggest common factor number is the GCF number.
So the greatest common factor 7686 and 7704 is 18.

Also check out the Least Common Multiple of 7686 and 7704