What is the Greatest Common Factor of 1089 and 1106?

Greatest common factor (GCF) of 1089 and 1106 is 1.

GCF(1089,1106) = 1

We will now calculate the prime factors of 1089 and 1106, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1089 and 1106.

How to find the GCF of 1089 and 1106?

We will first find the prime factorization of 1089 and 1106. After we will calculate the factors of 1089 and 1106 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 1106

Prime factors of 1106 are 2, 7, 79. Prime factorization of 1106 in exponential form is:

1106 = 2¹ × 7¹ × 79¹

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 1106

List of positive integer factors of 1106 that divides 1089 without a remainder.

1, 2, 7, 14, 79, 158, 553

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1089 and 1106. The biggest common factor number is the GCF number.
So the greatest common factor 1089 and 1106 is 1.

Also check out the Least Common Multiple of 1089 and 1106