What is the Greatest Common Factor of 9991 and 10005?

Greatest common factor (GCF) of 9991 and 10005 is 1.

GCF(9991,10005) = 1

We will now calculate the prime factors of 9991 and 10005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9991 and 10005.

How to find the GCF of 9991 and 10005?

We will first find the prime factorization of 9991 and 10005. After we will calculate the factors of 9991 and 10005 and find the biggest common factor number .

Step-1: Prime Factorization of 9991

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

9991 = 97¹ × 103¹

Step-2: Prime Factorization of 10005

Prime factors of 10005 are 3, 5, 23, 29. Prime factorization of 10005 in exponential form is:

10005 = 3¹ × 5¹ × 23¹ × 29¹

Step-3: Factors of 9991

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

1, 97, 103

Step-4: Factors of 10005

List of positive integer factors of 10005 that divides 9991 without a remainder.

1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9991 and 10005. The biggest common factor number is the GCF number.
So the greatest common factor 9991 and 10005 is 1.

Also check out the Least Common Multiple of 9991 and 10005