What is the Greatest Common Factor of 9684 and 9702?

Greatest common factor (GCF) of 9684 and 9702 is 18.

GCF(9684,9702) = 18

We will now calculate the prime factors of 9684 and 9702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9684 and 9702.

How to find the GCF of 9684 and 9702?

We will first find the prime factorization of 9684 and 9702. After we will calculate the factors of 9684 and 9702 and find the biggest common factor number .

Step-1: Prime Factorization of 9684

Prime factors of 9684 are 2, 3, 269. Prime factorization of 9684 in exponential form is:

9684 = 2² × 3² × 269¹

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 9684

List of positive integer factors of 9684 that divides 9684 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 269, 538, 807, 1076, 1614, 2421, 3228, 4842

Step-4: Factors of 9702

List of positive integer factors of 9702 that divides 9684 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 9684 and 9702. The biggest common factor number is the GCF number.
So the greatest common factor 9684 and 9702 is 18.

Also check out the Least Common Multiple of 9684 and 9702