What is the Greatest Common Factor of 7290 and 7296?

Greatest common factor (GCF) of 7290 and 7296 is 6.

GCF(7290,7296) = 6

We will now calculate the prime factors of 7290 and 7296, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7290 and 7296.

How to find the GCF of 7290 and 7296?

We will first find the prime factorization of 7290 and 7296. After we will calculate the factors of 7290 and 7296 and find the biggest common factor number .

Step-1: Prime Factorization of 7290

Prime factors of 7290 are 2, 3, 5. Prime factorization of 7290 in exponential form is:

7290 = 2¹ × 3⁶ × 5¹

Step-2: 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-3: Factors of 7290

List of positive integer factors of 7290 that divides 7290 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 729, 810, 1215, 1458, 2430, 3645

Step-4: Factors of 7296

List of positive integer factors of 7296 that divides 7290 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7290 and 7296. The biggest common factor number is the GCF number.
So the greatest common factor 7290 and 7296 is 6.

Also check out the Least Common Multiple of 7290 and 7296