What is the Greatest Common Factor of 2272 and 2288?

Greatest common factor (GCF) of 2272 and 2288 is 16.

GCF(2272,2288) = 16

We will now calculate the prime factors of 2272 and 2288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2272 and 2288.

How to find the GCF of 2272 and 2288?

We will first find the prime factorization of 2272 and 2288. After we will calculate the factors of 2272 and 2288 and find the biggest common factor number .

Step-1: Prime Factorization of 2272

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

2272 = 2⁵ × 71¹

Step-2: Prime Factorization of 2288

Prime factors of 2288 are 2, 11, 13. Prime factorization of 2288 in exponential form is:

2288 = 2⁴ × 11¹ × 13¹

Step-3: Factors of 2272

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

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

Step-4: Factors of 2288

List of positive integer factors of 2288 that divides 2272 without a remainder.

1, 2, 4, 8, 11, 13, 16, 22, 26, 44, 52, 88, 104, 143, 176, 208, 286, 572, 1144

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2272 and 2288. The biggest common factor number is the GCF number.
So the greatest common factor 2272 and 2288 is 16.

Also check out the Least Common Multiple of 2272 and 2288