What is the Greatest Common Factor of 19296 and 19305?

Greatest common factor (GCF) of 19296 and 19305 is 9.

GCF(19296,19305) = 9

We will now calculate the prime factors of 19296 and 19305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19296 and 19305.

How to find the GCF of 19296 and 19305?

We will first find the prime factorization of 19296 and 19305. After we will calculate the factors of 19296 and 19305 and find the biggest common factor number .

Step-1: Prime Factorization of 19296

Prime factors of 19296 are 2, 3, 67. Prime factorization of 19296 in exponential form is:

19296 = 2⁵ × 3² × 67¹

Step-2: Prime Factorization of 19305

Prime factors of 19305 are 3, 5, 11, 13. Prime factorization of 19305 in exponential form is:

19305 = 3³ × 5¹ × 11¹ × 13¹

Step-3: Factors of 19296

List of positive integer factors of 19296 that divides 19296 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 67, 72, 96, 134, 144, 201, 268, 288, 402, 536, 603, 804, 1072, 1206, 1608, 2144, 2412, 3216, 4824, 6432, 9648

Step-4: Factors of 19305

List of positive integer factors of 19305 that divides 19296 without a remainder.

1, 3, 5, 9, 11, 13, 15, 27, 33, 39, 45, 55, 65, 99, 117, 135, 143, 165, 195, 297, 351, 429, 495, 585, 715, 1287, 1485, 1755, 2145, 3861, 6435

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19296 and 19305. The biggest common factor number is the GCF number.
So the greatest common factor 19296 and 19305 is 9.

Also check out the Least Common Multiple of 19296 and 19305