What is the Greatest Common Factor of 7296 and 7302?

Greatest common factor (GCF) of 7296 and 7302 is 6.

GCF(7296,7302) = 6

We will now calculate the prime factors of 7296 and 7302, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7296 and 7302.

How to find the GCF of 7296 and 7302?

We will first find the prime factorization of 7296 and 7302. After we will calculate the factors of 7296 and 7302 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 7302

Prime factors of 7302 are 2, 3, 1217. Prime factorization of 7302 in exponential form is:

7302 = 2¹ × 3¹ × 1217¹

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 7302

List of positive integer factors of 7302 that divides 7296 without a remainder.

1, 2, 3, 6, 1217, 2434, 3651

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7296 and 7302. The biggest common factor number is the GCF number.
So the greatest common factor 7296 and 7302 is 6.

Also check out the Least Common Multiple of 7296 and 7302