What is the Greatest Common Factor of 7667 and 7684?

Greatest common factor (GCF) of 7667 and 7684 is 17.

GCF(7667,7684) = 17

We will now calculate the prime factors of 7667 and 7684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7667 and 7684.

How to find the GCF of 7667 and 7684?

We will first find the prime factorization of 7667 and 7684. After we will calculate the factors of 7667 and 7684 and find the biggest common factor number .

Step-1: Prime Factorization of 7667

Prime factors of 7667 are 11, 17, 41. Prime factorization of 7667 in exponential form is:

7667 = 11¹ × 17¹ × 41¹

Step-2: Prime Factorization of 7684

Prime factors of 7684 are 2, 17, 113. Prime factorization of 7684 in exponential form is:

7684 = 2² × 17¹ × 113¹

Step-3: Factors of 7667

List of positive integer factors of 7667 that divides 7667 without a remainder.

1, 11, 17, 41, 187, 451, 697

Step-4: Factors of 7684

List of positive integer factors of 7684 that divides 7667 without a remainder.

1, 2, 4, 17, 34, 68, 113, 226, 452, 1921, 3842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7667 and 7684. The biggest common factor number is the GCF number.
So the greatest common factor 7667 and 7684 is 17.

Also check out the Least Common Multiple of 7667 and 7684