What is the Greatest Common Factor of 81991 and 82000?

Greatest common factor (GCF) of 81991 and 82000 is 1.

GCF(81991,82000) = 1

We will now calculate the prime factors of 81991 and 82000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81991 and 82000.

How to find the GCF of 81991 and 82000?

We will first find the prime factorization of 81991 and 82000. After we will calculate the factors of 81991 and 82000 and find the biggest common factor number .

Step-1: Prime Factorization of 81991

Prime factors of 81991 are 7, 13, 17, 53. Prime factorization of 81991 in exponential form is:

81991 = 7¹ × 13¹ × 17¹ × 53¹

Step-2: 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-3: Factors of 81991

List of positive integer factors of 81991 that divides 81991 without a remainder.

1, 7, 13, 17, 53, 91, 119, 221, 371, 689, 901, 1547, 4823, 6307, 11713

Step-4: Factors of 82000

List of positive integer factors of 82000 that divides 81991 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81991 and 82000. The biggest common factor number is the GCF number.
So the greatest common factor 81991 and 82000 is 1.

Also check out the Least Common Multiple of 81991 and 82000