What is the Greatest Common Factor of 2254 and 2272?

Greatest common factor (GCF) of 2254 and 2272 is 2.

GCF(2254,2272) = 2

We will now calculate the prime factors of 2254 and 2272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2254 and 2272.

How to find the GCF of 2254 and 2272?

We will first find the prime factorization of 2254 and 2272. After we will calculate the factors of 2254 and 2272 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 2272

Prime factors of 2272 are 2, 71. Prime factorization of 2272 in exponential form is:

2272 = 2⁵ × 71¹

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 2272

List of positive integer factors of 2272 that divides 2254 without a remainder.

1, 2, 4, 8, 16, 32, 71, 142, 284, 568, 1136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2254 and 2272. The biggest common factor number is the GCF number.
So the greatest common factor 2254 and 2272 is 2.

Also check out the Least Common Multiple of 2254 and 2272