What is the Greatest Common Factor of 1089 and 1104?

Greatest common factor (GCF) of 1089 and 1104 is 3.

GCF(1089,1104) = 3

We will now calculate the prime factors of 1089 and 1104, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1089 and 1104.

How to find the GCF of 1089 and 1104?

We will first find the prime factorization of 1089 and 1104. After we will calculate the factors of 1089 and 1104 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 1104

Prime factors of 1104 are 2, 3, 23. Prime factorization of 1104 in exponential form is:

1104 = 2⁴ × 3¹ × 23¹

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 1104

List of positive integer factors of 1104 that divides 1089 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 69, 92, 138, 184, 276, 368, 552

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1089 and 1104. The biggest common factor number is the GCF number.
So the greatest common factor 1089 and 1104 is 3.

Also check out the Least Common Multiple of 1089 and 1104