What is the Greatest Common Factor of 13600 and 13617?

Greatest common factor (GCF) of 13600 and 13617 is 17.

GCF(13600,13617) = 17

We will now calculate the prime factors of 13600 and 13617, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13600 and 13617.

How to find the GCF of 13600 and 13617?

We will first find the prime factorization of 13600 and 13617. After we will calculate the factors of 13600 and 13617 and find the biggest common factor number .

Step-1: Prime Factorization of 13600

Prime factors of 13600 are 2, 5, 17. Prime factorization of 13600 in exponential form is:

13600 = 2⁵ × 5² × 17¹

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 13600

List of positive integer factors of 13600 that divides 13600 without a remainder.

1, 2, 4, 5, 8, 10, 16, 17, 20, 25, 32, 34, 40, 50, 68, 80, 85, 100, 136, 160, 170, 200, 272, 340, 400, 425, 544, 680, 800, 850, 1360, 1700, 2720, 3400, 6800

Step-4: Factors of 13617

List of positive integer factors of 13617 that divides 13600 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 13600 and 13617. The biggest common factor number is the GCF number.
So the greatest common factor 13600 and 13617 is 17.

Also check out the Least Common Multiple of 13600 and 13617