What is the Greatest Common Factor of 19984 and 20000?

Greatest common factor (GCF) of 19984 and 20000 is 16.

GCF(19984,20000) = 16

We will now calculate the prime factors of 19984 and 20000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19984 and 20000.

How to find the GCF of 19984 and 20000?

We will first find the prime factorization of 19984 and 20000. After we will calculate the factors of 19984 and 20000 and find the biggest common factor number .

Step-1: Prime Factorization of 19984

Prime factors of 19984 are 2, 1249. Prime factorization of 19984 in exponential form is:

19984 = 2⁴ × 1249¹

Step-2: Prime Factorization of 20000

Prime factors of 20000 are 2, 5. Prime factorization of 20000 in exponential form is:

20000 = 2⁵ × 5⁴

Step-3: Factors of 19984

List of positive integer factors of 19984 that divides 19984 without a remainder.

1, 2, 4, 8, 16, 1249, 2498, 4996, 9992

Step-4: Factors of 20000

List of positive integer factors of 20000 that divides 19984 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 4000, 5000, 10000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19984 and 20000. The biggest common factor number is the GCF number.
So the greatest common factor 19984 and 20000 is 16.

Also check out the Least Common Multiple of 19984 and 20000