What is the Greatest Common Factor of 11565 and 11583?

Greatest common factor (GCF) of 11565 and 11583 is 9.

GCF(11565,11583) = 9

We will now calculate the prime factors of 11565 and 11583, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 11565 and 11583.

How to find the GCF of 11565 and 11583?

We will first find the prime factorization of 11565 and 11583. After we will calculate the factors of 11565 and 11583 and find the biggest common factor number .

Step-1: Prime Factorization of 11565

Prime factors of 11565 are 3, 5, 257. Prime factorization of 11565 in exponential form is:

11565 = 3² × 5¹ × 257¹

Step-2: Prime Factorization of 11583

Prime factors of 11583 are 3, 11, 13. Prime factorization of 11583 in exponential form is:

11583 = 3⁴ × 11¹ × 13¹

Step-3: Factors of 11565

List of positive integer factors of 11565 that divides 11565 without a remainder.

1, 3, 5, 9, 15, 45, 257, 771, 1285, 2313, 3855

Step-4: Factors of 11583

List of positive integer factors of 11583 that divides 11565 without a remainder.

1, 3, 9, 11, 13, 27, 33, 39, 81, 99, 117, 143, 297, 351, 429, 891, 1053, 1287, 3861

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 11565 and 11583. The biggest common factor number is the GCF number.
So the greatest common factor 11565 and 11583 is 9.

Also check out the Least Common Multiple of 11565 and 11583