What is the Greatest Common Factor of 9971 and 9989?

Greatest common factor (GCF) of 9971 and 9989 is 1.

GCF(9971,9989) = 1

We will now calculate the prime factors of 9971 and 9989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9971 and 9989.

How to find the GCF of 9971 and 9989?

We will first find the prime factorization of 9971 and 9989. After we will calculate the factors of 9971 and 9989 and find the biggest common factor number .

Step-1: Prime Factorization of 9971

Prime factors of 9971 are 13, 59. Prime factorization of 9971 in exponential form is:

9971 = 13² × 59¹

Step-2: Prime Factorization of 9989

Prime factors of 9989 are 7, 1427. Prime factorization of 9989 in exponential form is:

9989 = 7¹ × 1427¹

Step-3: Factors of 9971

List of positive integer factors of 9971 that divides 9971 without a remainder.

1, 13, 59, 169, 767

Step-4: Factors of 9989

List of positive integer factors of 9989 that divides 9971 without a remainder.

1, 7, 1427

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9971 and 9989. The biggest common factor number is the GCF number.
So the greatest common factor 9971 and 9989 is 1.

Also check out the Least Common Multiple of 9971 and 9989