What is the Greatest Common Factor of 7296 and 7312?

Greatest common factor (GCF) of 7296 and 7312 is 16.

GCF(7296,7312) = 16

We will now calculate the prime factors of 7296 and 7312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7296 and 7312.

How to find the GCF of 7296 and 7312?

We will first find the prime factorization of 7296 and 7312. After we will calculate the factors of 7296 and 7312 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 7312

Prime factors of 7312 are 2, 457. Prime factorization of 7312 in exponential form is:

7312 = 2⁴ × 457¹

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 7312

List of positive integer factors of 7312 that divides 7296 without a remainder.

1, 2, 4, 8, 16, 457, 914, 1828, 3656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7296 and 7312. The biggest common factor number is the GCF number.
So the greatest common factor 7296 and 7312 is 16.

Also check out the Least Common Multiple of 7296 and 7312