What is the Greatest Common Factor of 9997 and 10010?

Greatest common factor (GCF) of 9997 and 10010 is 13.

GCF(9997,10010) = 13

We will now calculate the prime factors of 9997 and 10010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9997 and 10010.

How to find the GCF of 9997 and 10010?

We will first find the prime factorization of 9997 and 10010. After we will calculate the factors of 9997 and 10010 and find the biggest common factor number .

Step-1: Prime Factorization of 9997

Prime factors of 9997 are 13, 769. Prime factorization of 9997 in exponential form is:

9997 = 13¹ × 769¹

Step-2: Prime Factorization of 10010

Prime factors of 10010 are 2, 5, 7, 11, 13. Prime factorization of 10010 in exponential form is:

10010 = 2¹ × 5¹ × 7¹ × 11¹ × 13¹

Step-3: Factors of 9997

List of positive integer factors of 9997 that divides 9997 without a remainder.

1, 13, 769

Step-4: Factors of 10010

List of positive integer factors of 10010 that divides 9997 without a remainder.

1, 2, 5, 7, 10, 11, 13, 14, 22, 26, 35, 55, 65, 70, 77, 91, 110, 130, 143, 154, 182, 286, 385, 455, 715, 770, 910, 1001, 1430, 2002, 5005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9997 and 10010. The biggest common factor number is the GCF number.
So the greatest common factor 9997 and 10010 is 13.

Also check out the Least Common Multiple of 9997 and 10010