What is the Greatest Common Factor of 17982 and 17997?

Greatest common factor (GCF) of 17982 and 17997 is 3.

GCF(17982,17997) = 3

We will now calculate the prime factors of 17982 and 17997, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17982 and 17997.

How to find the GCF of 17982 and 17997?

We will first find the prime factorization of 17982 and 17997. After we will calculate the factors of 17982 and 17997 and find the biggest common factor number .

Step-1: Prime Factorization of 17982

Prime factors of 17982 are 2, 3, 37. Prime factorization of 17982 in exponential form is:

17982 = 2¹ × 3⁵ × 37¹

Step-2: Prime Factorization of 17997

Prime factors of 17997 are 3, 7, 857. Prime factorization of 17997 in exponential form is:

17997 = 3¹ × 7¹ × 857¹

Step-3: Factors of 17982

List of positive integer factors of 17982 that divides 17982 without a remainder.

1, 2, 3, 6, 9, 18, 27, 37, 54, 74, 81, 111, 162, 222, 243, 333, 486, 666, 999, 1998, 2997, 5994, 8991

Step-4: Factors of 17997

List of positive integer factors of 17997 that divides 17982 without a remainder.

1, 3, 7, 21, 857, 2571, 5999

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17982 and 17997. The biggest common factor number is the GCF number.
So the greatest common factor 17982 and 17997 is 3.

Also check out the Least Common Multiple of 17982 and 17997