What is the Greatest Common Factor of 81991 and 82005?

Greatest common factor (GCF) of 81991 and 82005 is 7.

GCF(81991,82005) = 7

We will now calculate the prime factors of 81991 and 82005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81991 and 82005.

How to find the GCF of 81991 and 82005?

We will first find the prime factorization of 81991 and 82005. After we will calculate the factors of 81991 and 82005 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 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 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 82005

List of positive integer factors of 82005 that divides 81991 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 81991 and 82005. The biggest common factor number is the GCF number.
So the greatest common factor 81991 and 82005 is 7.

Also check out the Least Common Multiple of 81991 and 82005