What is the Greatest Common Factor of 21989 and 22008?

Greatest common factor (GCF) of 21989 and 22008 is 1.

GCF(21989,22008) = 1

We will now calculate the prime factors of 21989 and 22008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21989 and 22008.

How to find the GCF of 21989 and 22008?

We will first find the prime factorization of 21989 and 22008. After we will calculate the factors of 21989 and 22008 and find the biggest common factor number .

Step-1: Prime Factorization of 21989

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

21989 = 11¹ × 1999¹

Step-2: Prime Factorization of 22008

Prime factors of 22008 are 2, 3, 7, 131. Prime factorization of 22008 in exponential form is:

22008 = 2³ × 3¹ × 7¹ × 131¹

Step-3: Factors of 21989

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

1, 11, 1999

Step-4: Factors of 22008

List of positive integer factors of 22008 that divides 21989 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 131, 168, 262, 393, 524, 786, 917, 1048, 1572, 1834, 2751, 3144, 3668, 5502, 7336, 11004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21989 and 22008. The biggest common factor number is the GCF number.
So the greatest common factor 21989 and 22008 is 1.

Also check out the Least Common Multiple of 21989 and 22008