What is the Greatest Common Factor of 13617 and 13634?

Greatest common factor (GCF) of 13617 and 13634 is 17.

GCF(13617,13634) = 17

We will now calculate the prime factors of 13617 and 13634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13617 and 13634.

How to find the GCF of 13617 and 13634?

We will first find the prime factorization of 13617 and 13634. After we will calculate the factors of 13617 and 13634 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 13634

Prime factors of 13634 are 2, 17, 401. Prime factorization of 13634 in exponential form is:

13634 = 2¹ × 17¹ × 401¹

Step-3: Factors of 13617

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

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

Step-4: Factors of 13634

List of positive integer factors of 13634 that divides 13617 without a remainder.

1, 2, 17, 34, 401, 802, 6817

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13617 and 13634. The biggest common factor number is the GCF number.
So the greatest common factor 13617 and 13634 is 17.

Also check out the Least Common Multiple of 13617 and 13634