What is the Greatest Common Factor of 9982 and 9996?

Greatest common factor (GCF) of 9982 and 9996 is 14.

GCF(9982,9996) = 14

We will now calculate the prime factors of 9982 and 9996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9982 and 9996.

How to find the GCF of 9982 and 9996?

We will first find the prime factorization of 9982 and 9996. After we will calculate the factors of 9982 and 9996 and find the biggest common factor number .

Step-1: Prime Factorization of 9982

Prime factors of 9982 are 2, 7, 23, 31. Prime factorization of 9982 in exponential form is:

9982 = 2¹ × 7¹ × 23¹ × 31¹

Step-2: Prime Factorization of 9996

Prime factors of 9996 are 2, 3, 7, 17. Prime factorization of 9996 in exponential form is:

9996 = 2² × 3¹ × 7² × 17¹

Step-3: Factors of 9982

List of positive integer factors of 9982 that divides 9982 without a remainder.

1, 2, 7, 14, 23, 31, 46, 62, 161, 217, 322, 434, 713, 1426, 4991

Step-4: Factors of 9996

List of positive integer factors of 9996 that divides 9982 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 49, 51, 68, 84, 98, 102, 119, 147, 196, 204, 238, 294, 357, 476, 588, 714, 833, 1428, 1666, 2499, 3332, 4998

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9982 and 9996. The biggest common factor number is the GCF number.
So the greatest common factor 9982 and 9996 is 14.

Also check out the Least Common Multiple of 9982 and 9996