What is the Greatest Common Factor of 1089 and 1109?

Greatest common factor (GCF) of 1089 and 1109 is 1.

GCF(1089,1109) = 1

We will now calculate the prime factors of 1089 and 1109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1089 and 1109.

How to find the GCF of 1089 and 1109?

We will first find the prime factorization of 1089 and 1109. After we will calculate the factors of 1089 and 1109 and find the biggest common factor number .

Step-1: Prime Factorization of 1089

Prime factors of 1089 are 3, 11. Prime factorization of 1089 in exponential form is:

1089 = 3² × 11²

Step-2: Prime Factorization of 1109

Prime factors of 1109 are 1109. Prime factorization of 1109 in exponential form is:

1109 = 1109¹

Step-3: Factors of 1089

List of positive integer factors of 1089 that divides 1089 without a remainder.

1, 3, 9, 11, 33, 99, 121, 363

Step-4: Factors of 1109

List of positive integer factors of 1109 that divides 1089 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1089 and 1109. The biggest common factor number is the GCF number.
So the greatest common factor 1089 and 1109 is 1.

Also check out the Least Common Multiple of 1089 and 1109