What is the Greatest Common Factor of 12896 and 12909?

Greatest common factor (GCF) of 12896 and 12909 is 13.

GCF(12896,12909) = 13

We will now calculate the prime factors of 12896 and 12909, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12896 and 12909.

How to find the GCF of 12896 and 12909?

We will first find the prime factorization of 12896 and 12909. After we will calculate the factors of 12896 and 12909 and find the biggest common factor number .

Step-1: Prime Factorization of 12896

Prime factors of 12896 are 2, 13, 31. Prime factorization of 12896 in exponential form is:

12896 = 2⁵ × 13¹ × 31¹

Step-2: Prime Factorization of 12909

Prime factors of 12909 are 3, 13, 331. Prime factorization of 12909 in exponential form is:

12909 = 3¹ × 13¹ × 331¹

Step-3: Factors of 12896

List of positive integer factors of 12896 that divides 12896 without a remainder.

1, 2, 4, 8, 13, 16, 26, 31, 32, 52, 62, 104, 124, 208, 248, 403, 416, 496, 806, 992, 1612, 3224, 6448

Step-4: Factors of 12909

List of positive integer factors of 12909 that divides 12896 without a remainder.

1, 3, 13, 39, 331, 993, 4303

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 12896 and 12909. The biggest common factor number is the GCF number.
So the greatest common factor 12896 and 12909 is 13.

Also check out the Least Common Multiple of 12896 and 12909