What is the Greatest Common Factor of 13605 and 13617?

Greatest common factor (GCF) of 13605 and 13617 is 3.

GCF(13605,13617) = 3

We will now calculate the prime factors of 13605 and 13617, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13605 and 13617.

How to find the GCF of 13605 and 13617?

We will first find the prime factorization of 13605 and 13617. After we will calculate the factors of 13605 and 13617 and find the biggest common factor number .

Step-1: Prime Factorization of 13605

Prime factors of 13605 are 3, 5, 907. Prime factorization of 13605 in exponential form is:

13605 = 3¹ × 5¹ × 907¹

Step-2: Prime Factorization of 13617

Prime factors of 13617 are 3, 17, 89. Prime factorization of 13617 in exponential form is:

13617 = 3² × 17¹ × 89¹

Step-3: Factors of 13605

List of positive integer factors of 13605 that divides 13605 without a remainder.

1, 3, 5, 15, 907, 2721, 4535

Step-4: Factors of 13617

List of positive integer factors of 13617 that divides 13605 without a remainder.

1, 3, 9, 17, 51, 89, 153, 267, 801, 1513, 4539

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13605 and 13617. The biggest common factor number is the GCF number.
So the greatest common factor 13605 and 13617 is 3.

Also check out the Least Common Multiple of 13605 and 13617