What is the Greatest Common Factor of 13685 and 13696?

Greatest common factor (GCF) of 13685 and 13696 is 1.

GCF(13685,13696) = 1

We will now calculate the prime factors of 13685 and 13696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13685 and 13696.

How to find the GCF of 13685 and 13696?

We will first find the prime factorization of 13685 and 13696. After we will calculate the factors of 13685 and 13696 and find the biggest common factor number .

Step-1: Prime Factorization of 13685

Prime factors of 13685 are 5, 7, 17, 23. Prime factorization of 13685 in exponential form is:

13685 = 5¹ × 7¹ × 17¹ × 23¹

Step-2: Prime Factorization of 13696

Prime factors of 13696 are 2, 107. Prime factorization of 13696 in exponential form is:

13696 = 2⁷ × 107¹

Step-3: Factors of 13685

List of positive integer factors of 13685 that divides 13685 without a remainder.

1, 5, 7, 17, 23, 35, 85, 115, 119, 161, 391, 595, 805, 1955, 2737

Step-4: Factors of 13696

List of positive integer factors of 13696 that divides 13685 without a remainder.

1, 2, 4, 8, 16, 32, 64, 107, 128, 214, 428, 856, 1712, 3424, 6848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13685 and 13696. The biggest common factor number is the GCF number.
So the greatest common factor 13685 and 13696 is 1.

Also check out the Least Common Multiple of 13685 and 13696