What is the Greatest Common Factor of 9984 and 9996?

Greatest common factor (GCF) of 9984 and 9996 is 12.

GCF(9984,9996) = 12

We will now calculate the prime factors of 9984 and 9996, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9984 and 9996.

How to find the GCF of 9984 and 9996?

We will first find the prime factorization of 9984 and 9996. After we will calculate the factors of 9984 and 9996 and find the biggest common factor number .

Step-1: Prime Factorization of 9984

Prime factors of 9984 are 2, 3, 13. Prime factorization of 9984 in exponential form is:

9984 = 2⁸ × 3¹ × 13¹

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 9984

List of positive integer factors of 9984 that divides 9984 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992

Step-4: Factors of 9996

List of positive integer factors of 9996 that divides 9984 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 9984 and 9996. The biggest common factor number is the GCF number.
So the greatest common factor 9984 and 9996 is 12.

Also check out the Least Common Multiple of 9984 and 9996