What is the Greatest Common Factor of 82005 and 82016?

Greatest common factor (GCF) of 82005 and 82016 is 11.

GCF(82005,82016) = 11

We will now calculate the prime factors of 82005 and 82016, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82005 and 82016.

How to find the GCF of 82005 and 82016?

We will first find the prime factorization of 82005 and 82016. After we will calculate the factors of 82005 and 82016 and find the biggest common factor number .

Step-1: Prime Factorization of 82005

Prime factors of 82005 are 3, 5, 7, 11, 71. Prime factorization of 82005 in exponential form is:

82005 = 3¹ × 5¹ × 7¹ × 11¹ × 71¹

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 82005

List of positive integer factors of 82005 that divides 82005 without a remainder.

1, 3, 5, 7, 11, 15, 21, 33, 35, 55, 71, 77, 105, 165, 213, 231, 355, 385, 497, 781, 1065, 1155, 1491, 2343, 2485, 3905, 5467, 7455, 11715, 16401, 27335

Step-4: Factors of 82016

List of positive integer factors of 82016 that divides 82005 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 82005 and 82016. The biggest common factor number is the GCF number.
So the greatest common factor 82005 and 82016 is 11.

Also check out the Least Common Multiple of 82005 and 82016