What is the Greatest Common Factor of 7275 and 7290?

Greatest common factor (GCF) of 7275 and 7290 is 15.

GCF(7275,7290) = 15

We will now calculate the prime factors of 7275 and 7290, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7275 and 7290.

How to find the GCF of 7275 and 7290?

We will first find the prime factorization of 7275 and 7290. After we will calculate the factors of 7275 and 7290 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 7290

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

7290 = 2¹ × 3⁶ × 5¹

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 7290

List of positive integer factors of 7290 that divides 7275 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7275 and 7290. The biggest common factor number is the GCF number.
So the greatest common factor 7275 and 7290 is 15.

Also check out the Least Common Multiple of 7275 and 7290