What is the Greatest Common Factor of 9984 and 10000?

Greatest common factor (GCF) of 9984 and 10000 is 16.

GCF(9984,10000) = 16

We will now calculate the prime factors of 9984 and 10000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9984 and 10000.

How to find the GCF of 9984 and 10000?

We will first find the prime factorization of 9984 and 10000. After we will calculate the factors of 9984 and 10000 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 10000

Prime factors of 10000 are 2, 5. Prime factorization of 10000 in exponential form is:

10000 = 2⁴ × 5⁴

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 10000

List of positive integer factors of 10000 that divides 9984 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9984 and 10000. The biggest common factor number is the GCF number.
So the greatest common factor 9984 and 10000 is 16.

Also check out the Least Common Multiple of 9984 and 10000