What is the Greatest Common Factor of 82000 and 82016?

Greatest common factor (GCF) of 82000 and 82016 is 16.

GCF(82000,82016) = 16

We will now calculate the prime factors of 82000 and 82016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82000 and 82016.

How to find the GCF of 82000 and 82016?

We will first find the prime factorization of 82000 and 82016. After we will calculate the factors of 82000 and 82016 and find the biggest common factor number .

Step-1: Prime Factorization of 82000

Prime factors of 82000 are 2, 5, 41. Prime factorization of 82000 in exponential form is:

82000 = 2⁴ × 5³ × 41¹

Step-2: Prime Factorization of 82016

Prime factors of 82016 are 2, 11, 233. Prime factorization of 82016 in exponential form is:

82016 = 2⁵ × 11¹ × 233¹

Step-3: Factors of 82000

List of positive integer factors of 82000 that divides 82000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 41, 50, 80, 82, 100, 125, 164, 200, 205, 250, 328, 400, 410, 500, 656, 820, 1000, 1025, 1640, 2000, 2050, 3280, 4100, 5125, 8200, 10250, 16400, 20500, 41000

Step-4: Factors of 82016

List of positive integer factors of 82016 that divides 82000 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 233, 352, 466, 932, 1864, 2563, 3728, 5126, 7456, 10252, 20504, 41008

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82000 and 82016. The biggest common factor number is the GCF number.
So the greatest common factor 82000 and 82016 is 16.

Also check out the Least Common Multiple of 82000 and 82016