What is the Greatest Common Factor of 9971 and 9991?

Greatest common factor (GCF) of 9971 and 9991 is 1.

GCF(9971,9991) = 1

We will now calculate the prime factors of 9971 and 9991, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9971 and 9991.

How to find the GCF of 9971 and 9991?

We will first find the prime factorization of 9971 and 9991. After we will calculate the factors of 9971 and 9991 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 9991

Prime factors of 9991 are 97, 103. Prime factorization of 9991 in exponential form is:

9991 = 97¹ × 103¹

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 9991

List of positive integer factors of 9991 that divides 9971 without a remainder.

1, 97, 103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9971 and 9991. The biggest common factor number is the GCF number.
So the greatest common factor 9971 and 9991 is 1.

Also check out the Least Common Multiple of 9971 and 9991