What is the Greatest Common Factor of 1089 and 1100?

Greatest common factor (GCF) of 1089 and 1100 is 11.

GCF(1089,1100) = 11

We will now calculate the prime factors of 1089 and 1100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1089 and 1100.

How to find the GCF of 1089 and 1100?

We will first find the prime factorization of 1089 and 1100. After we will calculate the factors of 1089 and 1100 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 1100

Prime factors of 1100 are 2, 5, 11. Prime factorization of 1100 in exponential form is:

1100 = 2² × 5² × 11¹

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 1100

List of positive integer factors of 1100 that divides 1089 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 220, 275, 550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1089 and 1100. The biggest common factor number is the GCF number.
So the greatest common factor 1089 and 1100 is 11.

Also check out the Least Common Multiple of 1089 and 1100