What is the Greatest Common Factor of 9686 and 9702?

Greatest common factor (GCF) of 9686 and 9702 is 2.

GCF(9686,9702) = 2

We will now calculate the prime factors of 9686 and 9702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9686 and 9702.

How to find the GCF of 9686 and 9702?

We will first find the prime factorization of 9686 and 9702. After we will calculate the factors of 9686 and 9702 and find the biggest common factor number .

Step-1: Prime Factorization of 9686

Prime factors of 9686 are 2, 29, 167. Prime factorization of 9686 in exponential form is:

9686 = 2¹ × 29¹ × 167¹

Step-2: Prime Factorization of 9702

Prime factors of 9702 are 2, 3, 7, 11. Prime factorization of 9702 in exponential form is:

9702 = 2¹ × 3² × 7² × 11¹

Step-3: Factors of 9686

List of positive integer factors of 9686 that divides 9686 without a remainder.

1, 2, 29, 58, 167, 334, 4843

Step-4: Factors of 9702

List of positive integer factors of 9702 that divides 9686 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 49, 63, 66, 77, 98, 99, 126, 147, 154, 198, 231, 294, 441, 462, 539, 693, 882, 1078, 1386, 1617, 3234, 4851

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9686 and 9702. The biggest common factor number is the GCF number.
So the greatest common factor 9686 and 9702 is 2.

Also check out the Least Common Multiple of 9686 and 9702