What is the Greatest Common Factor of 2265 and 2280?

Greatest common factor (GCF) of 2265 and 2280 is 15.

GCF(2265,2280) = 15

We will now calculate the prime factors of 2265 and 2280, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2265 and 2280.

How to find the GCF of 2265 and 2280?

We will first find the prime factorization of 2265 and 2280. After we will calculate the factors of 2265 and 2280 and find the biggest common factor number .

Step-1: Prime Factorization of 2265

Prime factors of 2265 are 3, 5, 151. Prime factorization of 2265 in exponential form is:

2265 = 3¹ × 5¹ × 151¹

Step-2: Prime Factorization of 2280

Prime factors of 2280 are 2, 3, 5, 19. Prime factorization of 2280 in exponential form is:

2280 = 2³ × 3¹ × 5¹ × 19¹

Step-3: Factors of 2265

List of positive integer factors of 2265 that divides 2265 without a remainder.

1, 3, 5, 15, 151, 453, 755

Step-4: Factors of 2280

List of positive integer factors of 2280 that divides 2265 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 19, 20, 24, 30, 38, 40, 57, 60, 76, 95, 114, 120, 152, 190, 228, 285, 380, 456, 570, 760, 1140

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2265 and 2280. The biggest common factor number is the GCF number.
So the greatest common factor 2265 and 2280 is 15.

Also check out the Least Common Multiple of 2265 and 2280