What is the Greatest Common Factor of 9971 and 9990?

Greatest common factor (GCF) of 9971 and 9990 is 1.

GCF(9971,9990) = 1

We will now calculate the prime factors of 9971 and 9990, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9971 and 9990.

How to find the GCF of 9971 and 9990?

We will first find the prime factorization of 9971 and 9990. After we will calculate the factors of 9971 and 9990 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 9990

Prime factors of 9990 are 2, 3, 5, 37. Prime factorization of 9990 in exponential form is:

9990 = 2¹ × 3³ × 5¹ × 37¹

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 9990

List of positive integer factors of 9990 that divides 9971 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 90, 111, 135, 185, 222, 270, 333, 370, 555, 666, 999, 1110, 1665, 1998, 3330, 4995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9971 and 9990. The biggest common factor number is the GCF number.
So the greatest common factor 9971 and 9990 is 1.

Also check out the Least Common Multiple of 9971 and 9990