What is the Greatest Common Factor of 19971 and 19977?

Greatest common factor (GCF) of 19971 and 19977 is 3.

GCF(19971,19977) = 3

We will now calculate the prime factors of 19971 and 19977, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19971 and 19977.

How to find the GCF of 19971 and 19977?

We will first find the prime factorization of 19971 and 19977. After we will calculate the factors of 19971 and 19977 and find the biggest common factor number .

Step-1: Prime Factorization of 19971

Prime factors of 19971 are 3, 7, 317. Prime factorization of 19971 in exponential form is:

19971 = 3² × 7¹ × 317¹

Step-2: Prime Factorization of 19977

Prime factors of 19977 are 3, 6659. Prime factorization of 19977 in exponential form is:

19977 = 3¹ × 6659¹

Step-3: Factors of 19971

List of positive integer factors of 19971 that divides 19971 without a remainder.

1, 3, 7, 9, 21, 63, 317, 951, 2219, 2853, 6657

Step-4: Factors of 19977

List of positive integer factors of 19977 that divides 19971 without a remainder.

1, 3, 6659

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19971 and 19977. The biggest common factor number is the GCF number.
So the greatest common factor 19971 and 19977 is 3.

Also check out the Least Common Multiple of 19971 and 19977