What is the Greatest Common Factor of 82000 and 82005?

Greatest common factor (GCF) of 82000 and 82005 is 5.

GCF(82000,82005) = 5

We will now calculate the prime factors of 82000 and 82005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82000 and 82005.

How to find the GCF of 82000 and 82005?

We will first find the prime factorization of 82000 and 82005. After we will calculate the factors of 82000 and 82005 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 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-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 82005

List of positive integer factors of 82005 that divides 82000 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82000 and 82005. The biggest common factor number is the GCF number.
So the greatest common factor 82000 and 82005 is 5.

Also check out the Least Common Multiple of 82000 and 82005