What is the Greatest Common Factor of 27993 and 28007?

Greatest common factor (GCF) of 27993 and 28007 is 7.

GCF(27993,28007) = 7

We will now calculate the prime factors of 27993 and 28007, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27993 and 28007.

How to find the GCF of 27993 and 28007?

We will first find the prime factorization of 27993 and 28007. After we will calculate the factors of 27993 and 28007 and find the biggest common factor number .

Step-1: Prime Factorization of 27993

Prime factors of 27993 are 3, 7, 31, 43. Prime factorization of 27993 in exponential form is:

27993 = 3¹ × 7¹ × 31¹ × 43¹

Step-2: Prime Factorization of 28007

Prime factors of 28007 are 7, 4001. Prime factorization of 28007 in exponential form is:

28007 = 7¹ × 4001¹

Step-3: Factors of 27993

List of positive integer factors of 27993 that divides 27993 without a remainder.

1, 3, 7, 21, 31, 43, 93, 129, 217, 301, 651, 903, 1333, 3999, 9331

Step-4: Factors of 28007

List of positive integer factors of 28007 that divides 27993 without a remainder.

1, 7, 4001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27993 and 28007. The biggest common factor number is the GCF number.
So the greatest common factor 27993 and 28007 is 7.

Also check out the Least Common Multiple of 27993 and 28007