What is the Greatest Common Factor of 21978 and 21989?

Greatest common factor (GCF) of 21978 and 21989 is 11.

GCF(21978,21989) = 11

We will now calculate the prime factors of 21978 and 21989, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21978 and 21989.

How to find the GCF of 21978 and 21989?

We will first find the prime factorization of 21978 and 21989. After we will calculate the factors of 21978 and 21989 and find the biggest common factor number .

Step-1: Prime Factorization of 21978

Prime factors of 21978 are 2, 3, 11, 37. Prime factorization of 21978 in exponential form is:

21978 = 2¹ × 3³ × 11¹ × 37¹

Step-2: Prime Factorization of 21989

Prime factors of 21989 are 11, 1999. Prime factorization of 21989 in exponential form is:

21989 = 11¹ × 1999¹

Step-3: Factors of 21978

List of positive integer factors of 21978 that divides 21978 without a remainder.

1, 2, 3, 6, 9, 11, 18, 22, 27, 33, 37, 54, 66, 74, 99, 111, 198, 222, 297, 333, 407, 594, 666, 814, 999, 1221, 1998, 2442, 3663, 7326, 10989

Step-4: Factors of 21989

List of positive integer factors of 21989 that divides 21978 without a remainder.

1, 11, 1999

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21978 and 21989. The biggest common factor number is the GCF number.
So the greatest common factor 21978 and 21989 is 11.

Also check out the Least Common Multiple of 21978 and 21989