What is the Greatest Common Factor of 13685 and 13702?

Greatest common factor (GCF) of 13685 and 13702 is 17.

GCF(13685,13702) = 17

We will now calculate the prime factors of 13685 and 13702, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13685 and 13702.

How to find the GCF of 13685 and 13702?

We will first find the prime factorization of 13685 and 13702. After we will calculate the factors of 13685 and 13702 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 13702

Prime factors of 13702 are 2, 13, 17, 31. Prime factorization of 13702 in exponential form is:

13702 = 2¹ × 13¹ × 17¹ × 31¹

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 13702

List of positive integer factors of 13702 that divides 13685 without a remainder.

1, 2, 13, 17, 26, 31, 34, 62, 221, 403, 442, 527, 806, 1054, 6851

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13685 and 13702. The biggest common factor number is the GCF number.
So the greatest common factor 13685 and 13702 is 17.

Also check out the Least Common Multiple of 13685 and 13702