What is the Greatest Common Factor of 7275 and 7280?

Greatest common factor (GCF) of 7275 and 7280 is 5.

GCF(7275,7280) = 5

We will now calculate the prime factors of 7275 and 7280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7275 and 7280.

How to find the GCF of 7275 and 7280?

We will first find the prime factorization of 7275 and 7280. After we will calculate the factors of 7275 and 7280 and find the biggest common factor number .

Step-1: Prime Factorization of 7275

Prime factors of 7275 are 3, 5, 97. Prime factorization of 7275 in exponential form is:

7275 = 3¹ × 5² × 97¹

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 7275

List of positive integer factors of 7275 that divides 7275 without a remainder.

1, 3, 5, 15, 25, 75, 97, 291, 485, 1455, 2425

Step-4: Factors of 7280

List of positive integer factors of 7280 that divides 7275 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 7275 and 7280. The biggest common factor number is the GCF number.
So the greatest common factor 7275 and 7280 is 5.

Also check out the Least Common Multiple of 7275 and 7280