What is the Greatest Common Factor of 13689 and 13706?

Greatest common factor (GCF) of 13689 and 13706 is 1.

GCF(13689,13706) = 1

We will now calculate the prime factors of 13689 and 13706, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13689 and 13706.

How to find the GCF of 13689 and 13706?

We will first find the prime factorization of 13689 and 13706. After we will calculate the factors of 13689 and 13706 and find the biggest common factor number .

Step-1: Prime Factorization of 13689

Prime factors of 13689 are 3, 13. Prime factorization of 13689 in exponential form is:

13689 = 3⁴ × 13²

Step-2: Prime Factorization of 13706

Prime factors of 13706 are 2, 7, 11, 89. Prime factorization of 13706 in exponential form is:

13706 = 2¹ × 7¹ × 11¹ × 89¹

Step-3: Factors of 13689

List of positive integer factors of 13689 that divides 13689 without a remainder.

1, 3, 9, 13, 27, 39, 81, 117, 169, 351, 507, 1053, 1521, 4563

Step-4: Factors of 13706

List of positive integer factors of 13706 that divides 13689 without a remainder.

1, 2, 7, 11, 14, 22, 77, 89, 154, 178, 623, 979, 1246, 1958, 6853

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13689 and 13706. The biggest common factor number is the GCF number.
So the greatest common factor 13689 and 13706 is 1.

Also check out the Least Common Multiple of 13689 and 13706