What is the Greatest Common Factor of 2254 and 2268?

Greatest common factor (GCF) of 2254 and 2268 is 14.

GCF(2254,2268) = 14

We will now calculate the prime factors of 2254 and 2268, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2254 and 2268.

How to find the GCF of 2254 and 2268?

We will first find the prime factorization of 2254 and 2268. After we will calculate the factors of 2254 and 2268 and find the biggest common factor number .

Step-1: Prime Factorization of 2254

Prime factors of 2254 are 2, 7, 23. Prime factorization of 2254 in exponential form is:

2254 = 2¹ × 7² × 23¹

Step-2: 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-3: Factors of 2254

List of positive integer factors of 2254 that divides 2254 without a remainder.

1, 2, 7, 14, 23, 46, 49, 98, 161, 322, 1127

Step-4: Factors of 2268

List of positive integer factors of 2268 that divides 2254 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2254 and 2268. The biggest common factor number is the GCF number.
So the greatest common factor 2254 and 2268 is 14.

Also check out the Least Common Multiple of 2254 and 2268