What is the Greatest Common Factor of 81991 and 82008?

Greatest common factor (GCF) of 81991 and 82008 is 17.

GCF(81991,82008) = 17

We will now calculate the prime factors of 81991 and 82008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81991 and 82008.

How to find the GCF of 81991 and 82008?

We will first find the prime factorization of 81991 and 82008. After we will calculate the factors of 81991 and 82008 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 82008

Prime factors of 82008 are 2, 3, 17, 67. Prime factorization of 82008 in exponential form is:

82008 = 2³ × 3² × 17¹ × 67¹

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 82008

List of positive integer factors of 82008 that divides 81991 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 17, 18, 24, 34, 36, 51, 67, 68, 72, 102, 134, 136, 153, 201, 204, 268, 306, 402, 408, 536, 603, 612, 804, 1139, 1206, 1224, 1608, 2278, 2412, 3417, 4556, 4824, 6834, 9112, 10251, 13668, 20502, 27336, 41004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81991 and 82008. The biggest common factor number is the GCF number.
So the greatest common factor 81991 and 82008 is 17.

Also check out the Least Common Multiple of 81991 and 82008