What is the Greatest Common Factor of 12993 and 13005?

Greatest common factor (GCF) of 12993 and 13005 is 3.

GCF(12993,13005) = 3

We will now calculate the prime factors of 12993 and 13005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12993 and 13005.

How to find the GCF of 12993 and 13005?

We will first find the prime factorization of 12993 and 13005. After we will calculate the factors of 12993 and 13005 and find the biggest common factor number .

Step-1: Prime Factorization of 12993

Prime factors of 12993 are 3, 61, 71. Prime factorization of 12993 in exponential form is:

12993 = 3¹ × 61¹ × 71¹

Step-2: Prime Factorization of 13005

Prime factors of 13005 are 3, 5, 17. Prime factorization of 13005 in exponential form is:

13005 = 3² × 5¹ × 17²

Step-3: Factors of 12993

List of positive integer factors of 12993 that divides 12993 without a remainder.

1, 3, 61, 71, 183, 213, 4331

Step-4: Factors of 13005

List of positive integer factors of 13005 that divides 12993 without a remainder.

1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 289, 765, 867, 1445, 2601, 4335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12993 and 13005. The biggest common factor number is the GCF number.
So the greatest common factor 12993 and 13005 is 3.

Also check out the Least Common Multiple of 12993 and 13005