What is the Greatest Common Factor of 21993 and 22005?

Greatest common factor (GCF) of 21993 and 22005 is 3.

GCF(21993,22005) = 3

We will now calculate the prime factors of 21993 and 22005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21993 and 22005.

How to find the GCF of 21993 and 22005?

We will first find the prime factorization of 21993 and 22005. After we will calculate the factors of 21993 and 22005 and find the biggest common factor number .

Step-1: Prime Factorization of 21993

Prime factors of 21993 are 3, 7331. Prime factorization of 21993 in exponential form is:

21993 = 3¹ × 7331¹

Step-2: Prime Factorization of 22005

Prime factors of 22005 are 3, 5, 163. Prime factorization of 22005 in exponential form is:

22005 = 3³ × 5¹ × 163¹

Step-3: Factors of 21993

List of positive integer factors of 21993 that divides 21993 without a remainder.

1, 3, 7331

Step-4: Factors of 22005

List of positive integer factors of 22005 that divides 21993 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135, 163, 489, 815, 1467, 2445, 4401, 7335

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21993 and 22005. The biggest common factor number is the GCF number.
So the greatest common factor 21993 and 22005 is 3.

Also check out the Least Common Multiple of 21993 and 22005