What is the Greatest Common Factor of 19966 and 19982?

Greatest common factor (GCF) of 19966 and 19982 is 2.

GCF(19966,19982) = 2

We will now calculate the prime factors of 19966 and 19982, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19966 and 19982.

How to find the GCF of 19966 and 19982?

We will first find the prime factorization of 19966 and 19982. After we will calculate the factors of 19966 and 19982 and find the biggest common factor number .

Step-1: Prime Factorization of 19966

Prime factors of 19966 are 2, 67, 149. Prime factorization of 19966 in exponential form is:

19966 = 2¹ × 67¹ × 149¹

Step-2: Prime Factorization of 19982

Prime factors of 19982 are 2, 97, 103. Prime factorization of 19982 in exponential form is:

19982 = 2¹ × 97¹ × 103¹

Step-3: Factors of 19966

List of positive integer factors of 19966 that divides 19966 without a remainder.

1, 2, 67, 134, 149, 298, 9983

Step-4: Factors of 19982

List of positive integer factors of 19982 that divides 19966 without a remainder.

1, 2, 97, 103, 194, 206, 9991

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19966 and 19982. The biggest common factor number is the GCF number.
So the greatest common factor 19966 and 19982 is 2.

Also check out the Least Common Multiple of 19966 and 19982