What is the Greatest Common Factor of 27993 and 28000?

Greatest common factor (GCF) of 27993 and 28000 is 7.

GCF(27993,28000) = 7

We will now calculate the prime factors of 27993 and 28000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27993 and 28000.

How to find the GCF of 27993 and 28000?

We will first find the prime factorization of 27993 and 28000. After we will calculate the factors of 27993 and 28000 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 28000

Prime factors of 28000 are 2, 5, 7. Prime factorization of 28000 in exponential form is:

28000 = 2⁵ × 5³ × 7¹

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 28000

List of positive integer factors of 28000 that divides 27993 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 50, 56, 70, 80, 100, 112, 125, 140, 160, 175, 200, 224, 250, 280, 350, 400, 500, 560, 700, 800, 875, 1000, 1120, 1400, 1750, 2000, 2800, 3500, 4000, 5600, 7000, 14000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27993 and 28000. The biggest common factor number is the GCF number.
So the greatest common factor 27993 and 28000 is 7.

Also check out the Least Common Multiple of 27993 and 28000