What is the Greatest Common Factor of 15982 and 16000?

Greatest common factor (GCF) of 15982 and 16000 is 2.

GCF(15982,16000) = 2

We will now calculate the prime factors of 15982 and 16000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 15982 and 16000.

How to find the GCF of 15982 and 16000?

We will first find the prime factorization of 15982 and 16000. After we will calculate the factors of 15982 and 16000 and find the biggest common factor number .

Step-1: Prime Factorization of 15982

Prime factors of 15982 are 2, 61, 131. Prime factorization of 15982 in exponential form is:

15982 = 2¹ × 61¹ × 131¹

Step-2: Prime Factorization of 16000

Prime factors of 16000 are 2, 5. Prime factorization of 16000 in exponential form is:

16000 = 2⁷ × 5³

Step-3: Factors of 15982

List of positive integer factors of 15982 that divides 15982 without a remainder.

1, 2, 61, 122, 131, 262, 7991

Step-4: Factors of 16000

List of positive integer factors of 16000 that divides 15982 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 320, 400, 500, 640, 800, 1000, 1600, 2000, 3200, 4000, 8000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 15982 and 16000. The biggest common factor number is the GCF number.
So the greatest common factor 15982 and 16000 is 2.

Also check out the Least Common Multiple of 15982 and 16000