What is the Greatest Common Factor of 2268 and 2275?

Greatest common factor (GCF) of 2268 and 2275 is 7.

GCF(2268,2275) = 7

We will now calculate the prime factors of 2268 and 2275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2268 and 2275.

How to find the GCF of 2268 and 2275?

We will first find the prime factorization of 2268 and 2275. After we will calculate the factors of 2268 and 2275 and find the biggest common factor number .

Step-1: Prime Factorization of 2268

Prime factors of 2268 are 2, 3, 7. Prime factorization of 2268 in exponential form is:

2268 = 2² × 3⁴ × 7¹

Step-2: Prime Factorization of 2275

Prime factors of 2275 are 5, 7, 13. Prime factorization of 2275 in exponential form is:

2275 = 5² × 7¹ × 13¹

Step-3: Factors of 2268

List of positive integer factors of 2268 that divides 2268 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 42, 54, 63, 81, 84, 108, 126, 162, 189, 252, 324, 378, 567, 756, 1134

Step-4: Factors of 2275

List of positive integer factors of 2275 that divides 2268 without a remainder.

1, 5, 7, 13, 25, 35, 65, 91, 175, 325, 455

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2268 and 2275. The biggest common factor number is the GCF number.
So the greatest common factor 2268 and 2275 is 7.

Also check out the Least Common Multiple of 2268 and 2275