What is the Greatest Common Factor of 2268 and 2282?

Greatest common factor (GCF) of 2268 and 2282 is 14.

GCF(2268,2282) = 14

We will now calculate the prime factors of 2268 and 2282, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2268 and 2282.

How to find the GCF of 2268 and 2282?

We will first find the prime factorization of 2268 and 2282. After we will calculate the factors of 2268 and 2282 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 2282

Prime factors of 2282 are 2, 7, 163. Prime factorization of 2282 in exponential form is:

2282 = 2¹ × 7¹ × 163¹

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 2282

List of positive integer factors of 2282 that divides 2268 without a remainder.

1, 2, 7, 14, 163, 326, 1141

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2268 and 2282. The biggest common factor number is the GCF number.
So the greatest common factor 2268 and 2282 is 14.

Also check out the Least Common Multiple of 2268 and 2282