What is the Greatest Common Factor of 1089 and 1107?

Greatest common factor (GCF) of 1089 and 1107 is 9.

GCF(1089,1107) = 9

We will now calculate the prime factors of 1089 and 1107, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1089 and 1107.

How to find the GCF of 1089 and 1107?

We will first find the prime factorization of 1089 and 1107. After we will calculate the factors of 1089 and 1107 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 1107

Prime factors of 1107 are 3, 41. Prime factorization of 1107 in exponential form is:

1107 = 3³ × 41¹

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 1107

List of positive integer factors of 1107 that divides 1089 without a remainder.

1, 3, 9, 27, 41, 123, 369

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1089 and 1107. The biggest common factor number is the GCF number.
So the greatest common factor 1089 and 1107 is 9.

Also check out the Least Common Multiple of 1089 and 1107