What is the Greatest Common Factor of 7264 and 7280?

Greatest common factor (GCF) of 7264 and 7280 is 16.

GCF(7264,7280) = 16

We will now calculate the prime factors of 7264 and 7280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7264 and 7280.

How to find the GCF of 7264 and 7280?

We will first find the prime factorization of 7264 and 7280. After we will calculate the factors of 7264 and 7280 and find the biggest common factor number .

Step-1: Prime Factorization of 7264

Prime factors of 7264 are 2, 227. Prime factorization of 7264 in exponential form is:

7264 = 2⁵ × 227¹

Step-2: Prime Factorization of 7280

Prime factors of 7280 are 2, 5, 7, 13. Prime factorization of 7280 in exponential form is:

7280 = 2⁴ × 5¹ × 7¹ × 13¹

Step-3: Factors of 7264

List of positive integer factors of 7264 that divides 7264 without a remainder.

1, 2, 4, 8, 16, 32, 227, 454, 908, 1816, 3632

Step-4: Factors of 7280

List of positive integer factors of 7280 that divides 7264 without a remainder.

1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 26, 28, 35, 40, 52, 56, 65, 70, 80, 91, 104, 112, 130, 140, 182, 208, 260, 280, 364, 455, 520, 560, 728, 910, 1040, 1456, 1820, 3640

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7264 and 7280. The biggest common factor number is the GCF number.
So the greatest common factor 7264 and 7280 is 16.

Also check out the Least Common Multiple of 7264 and 7280