What is the Greatest Common Factor of 7686 and 7705?

Greatest common factor (GCF) of 7686 and 7705 is 1.

GCF(7686,7705) = 1

We will now calculate the prime factors of 7686 and 7705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7686 and 7705.

How to find the GCF of 7686 and 7705?

We will first find the prime factorization of 7686 and 7705. After we will calculate the factors of 7686 and 7705 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 7705

Prime factors of 7705 are 5, 23, 67. Prime factorization of 7705 in exponential form is:

7705 = 5¹ × 23¹ × 67¹

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 7705

List of positive integer factors of 7705 that divides 7686 without a remainder.

1, 5, 23, 67, 115, 335, 1541

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7686 and 7705. The biggest common factor number is the GCF number.
So the greatest common factor 7686 and 7705 is 1.

Also check out the Least Common Multiple of 7686 and 7705