What is the Greatest Common Factor of 7296 and 7305?

Greatest common factor (GCF) of 7296 and 7305 is 3.

GCF(7296,7305) = 3

We will now calculate the prime factors of 7296 and 7305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7296 and 7305.

How to find the GCF of 7296 and 7305?

We will first find the prime factorization of 7296 and 7305. After we will calculate the factors of 7296 and 7305 and find the biggest common factor number .

Step-1: Prime Factorization of 7296

Prime factors of 7296 are 2, 3, 19. Prime factorization of 7296 in exponential form is:

7296 = 2⁷ × 3¹ × 19¹

Step-2: Prime Factorization of 7305

Prime factors of 7305 are 3, 5, 487. Prime factorization of 7305 in exponential form is:

7305 = 3¹ × 5¹ × 487¹

Step-3: Factors of 7296

List of positive integer factors of 7296 that divides 7296 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 128, 152, 192, 228, 304, 384, 456, 608, 912, 1216, 1824, 2432, 3648

Step-4: Factors of 7305

List of positive integer factors of 7305 that divides 7296 without a remainder.

1, 3, 5, 15, 487, 1461, 2435

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7296 and 7305. The biggest common factor number is the GCF number.
So the greatest common factor 7296 and 7305 is 3.

Also check out the Least Common Multiple of 7296 and 7305