What is the Greatest Common Factor of 7674 and 7686?

Greatest common factor (GCF) of 7674 and 7686 is 6.

GCF(7674,7686) = 6

We will now calculate the prime factors of 7674 and 7686, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7674 and 7686.

How to find the GCF of 7674 and 7686?

We will first find the prime factorization of 7674 and 7686. After we will calculate the factors of 7674 and 7686 and find the biggest common factor number .

Step-1: Prime Factorization of 7674

Prime factors of 7674 are 2, 3, 1279. Prime factorization of 7674 in exponential form is:

7674 = 2¹ × 3¹ × 1279¹

Step-2: 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-3: Factors of 7674

List of positive integer factors of 7674 that divides 7674 without a remainder.

1, 2, 3, 6, 1279, 2558, 3837

Step-4: Factors of 7686

List of positive integer factors of 7686 that divides 7674 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7674 and 7686. The biggest common factor number is the GCF number.
So the greatest common factor 7674 and 7686 is 6.

Also check out the Least Common Multiple of 7674 and 7686