What is the Greatest Common Factor of 17978 and 17982?

Greatest common factor (GCF) of 17978 and 17982 is 2.

GCF(17978,17982) = 2

We will now calculate the prime factors of 17978 and 17982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17978 and 17982.

How to find the GCF of 17978 and 17982?

We will first find the prime factorization of 17978 and 17982. After we will calculate the factors of 17978 and 17982 and find the biggest common factor number .

Step-1: Prime Factorization of 17978

Prime factors of 17978 are 2, 89, 101. Prime factorization of 17978 in exponential form is:

17978 = 2¹ × 89¹ × 101¹

Step-2: 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-3: Factors of 17978

List of positive integer factors of 17978 that divides 17978 without a remainder.

1, 2, 89, 101, 178, 202, 8989

Step-4: Factors of 17982

List of positive integer factors of 17982 that divides 17978 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17978 and 17982. The biggest common factor number is the GCF number.
So the greatest common factor 17978 and 17982 is 2.

Also check out the Least Common Multiple of 17978 and 17982