What is the Greatest Common Factor of 22089 and 22100?

Greatest common factor (GCF) of 22089 and 22100 is 1.

GCF(22089,22100) = 1

We will now calculate the prime factors of 22089 and 22100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22089 and 22100.

How to find the GCF of 22089 and 22100?

We will first find the prime factorization of 22089 and 22100. After we will calculate the factors of 22089 and 22100 and find the biggest common factor number .

Step-1: Prime Factorization of 22089

Prime factors of 22089 are 3, 37, 199. Prime factorization of 22089 in exponential form is:

22089 = 3¹ × 37¹ × 199¹

Step-2: Prime Factorization of 22100

Prime factors of 22100 are 2, 5, 13, 17. Prime factorization of 22100 in exponential form is:

22100 = 2² × 5² × 13¹ × 17¹

Step-3: Factors of 22089

List of positive integer factors of 22089 that divides 22089 without a remainder.

1, 3, 37, 111, 199, 597, 7363

Step-4: Factors of 22100

List of positive integer factors of 22100 that divides 22089 without a remainder.

1, 2, 4, 5, 10, 13, 17, 20, 25, 26, 34, 50, 52, 65, 68, 85, 100, 130, 170, 221, 260, 325, 340, 425, 442, 650, 850, 884, 1105, 1300, 1700, 2210, 4420, 5525, 11050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22089 and 22100. The biggest common factor number is the GCF number.
So the greatest common factor 22089 and 22100 is 1.

Also check out the Least Common Multiple of 22089 and 22100