What is the Greatest Common Factor of 9982 and 10000?

Greatest common factor (GCF) of 9982 and 10000 is 2.

GCF(9982,10000) = 2

We will now calculate the prime factors of 9982 and 10000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9982 and 10000.

How to find the GCF of 9982 and 10000?

We will first find the prime factorization of 9982 and 10000. After we will calculate the factors of 9982 and 10000 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 10000

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

10000 = 2⁴ × 5⁴

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 10000

List of positive integer factors of 10000 that divides 9982 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 9982 and 10000. The biggest common factor number is the GCF number.
So the greatest common factor 9982 and 10000 is 2.

Also check out the Least Common Multiple of 9982 and 10000