What is the Greatest Common Factor of 25792 and 25805?

Greatest common factor (GCF) of 25792 and 25805 is 13.

GCF(25792,25805) = 13

We will now calculate the prime factors of 25792 and 25805, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25792 and 25805.

How to find the GCF of 25792 and 25805?

We will first find the prime factorization of 25792 and 25805. After we will calculate the factors of 25792 and 25805 and find the biggest common factor number .

Step-1: Prime Factorization of 25792

Prime factors of 25792 are 2, 13, 31. Prime factorization of 25792 in exponential form is:

25792 = 2⁶ × 13¹ × 31¹

Step-2: Prime Factorization of 25805

Prime factors of 25805 are 5, 13, 397. Prime factorization of 25805 in exponential form is:

25805 = 5¹ × 13¹ × 397¹

Step-3: Factors of 25792

List of positive integer factors of 25792 that divides 25792 without a remainder.

1, 2, 4, 8, 13, 16, 26, 31, 32, 52, 62, 64, 104, 124, 208, 248, 403, 416, 496, 806, 832, 992, 1612, 1984, 3224, 6448, 12896

Step-4: Factors of 25805

List of positive integer factors of 25805 that divides 25792 without a remainder.

1, 5, 13, 65, 397, 1985, 5161

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25792 and 25805. The biggest common factor number is the GCF number.
So the greatest common factor 25792 and 25805 is 13.

Also check out the Least Common Multiple of 25792 and 25805