What is the Greatest Common Factor of 26289 and 26304?

Greatest common factor (GCF) of 26289 and 26304 is 3.

GCF(26289,26304) = 3

We will now calculate the prime factors of 26289 and 26304, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 26289 and 26304.

How to find the GCF of 26289 and 26304?

We will first find the prime factorization of 26289 and 26304. After we will calculate the factors of 26289 and 26304 and find the biggest common factor number .

Step-1: Prime Factorization of 26289

Prime factors of 26289 are 3, 23, 127. Prime factorization of 26289 in exponential form is:

26289 = 3² × 23¹ × 127¹

Step-2: Prime Factorization of 26304

Prime factors of 26304 are 2, 3, 137. Prime factorization of 26304 in exponential form is:

26304 = 2⁶ × 3¹ × 137¹

Step-3: Factors of 26289

List of positive integer factors of 26289 that divides 26289 without a remainder.

1, 3, 9, 23, 69, 127, 207, 381, 1143, 2921, 8763

Step-4: Factors of 26304

List of positive integer factors of 26304 that divides 26289 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 137, 192, 274, 411, 548, 822, 1096, 1644, 2192, 3288, 4384, 6576, 8768, 13152

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 26289 and 26304. The biggest common factor number is the GCF number.
So the greatest common factor 26289 and 26304 is 3.

Also check out the Least Common Multiple of 26289 and 26304