What is the Greatest Common Factor of 82000 and 82017?

Greatest common factor (GCF) of 82000 and 82017 is 1.

GCF(82000,82017) = 1

We will now calculate the prime factors of 82000 and 82017, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82000 and 82017.

How to find the GCF of 82000 and 82017?

We will first find the prime factorization of 82000 and 82017. After we will calculate the factors of 82000 and 82017 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 82017

Prime factors of 82017 are 3, 13, 701. Prime factorization of 82017 in exponential form is:

82017 = 3² × 13¹ × 701¹

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 82017

List of positive integer factors of 82017 that divides 82000 without a remainder.

1, 3, 9, 13, 39, 117, 701, 2103, 6309, 9113, 27339

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82000 and 82017. The biggest common factor number is the GCF number.
So the greatest common factor 82000 and 82017 is 1.

Also check out the Least Common Multiple of 82000 and 82017