What is the Greatest Common Factor of 2208 and 2228?

Greatest common factor (GCF) of 2208 and 2228 is 4.

GCF(2208,2228) = 4

We will now calculate the prime factors of 2208 and 2228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2208 and 2228.

How to find the GCF of 2208 and 2228?

We will first find the prime factorization of 2208 and 2228. After we will calculate the factors of 2208 and 2228 and find the biggest common factor number .

Step-1: Prime Factorization of 2208

Prime factors of 2208 are 2, 3, 23. Prime factorization of 2208 in exponential form is:

2208 = 2⁵ × 3¹ × 23¹

Step-2: Prime Factorization of 2228

Prime factors of 2228 are 2, 557. Prime factorization of 2228 in exponential form is:

2228 = 2² × 557¹

Step-3: Factors of 2208

List of positive integer factors of 2208 that divides 2208 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 32, 46, 48, 69, 92, 96, 138, 184, 276, 368, 552, 736, 1104

Step-4: Factors of 2228

List of positive integer factors of 2228 that divides 2208 without a remainder.

1, 2, 4, 557, 1114

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2208 and 2228. The biggest common factor number is the GCF number.
So the greatest common factor 2208 and 2228 is 4.

Also check out the Least Common Multiple of 2208 and 2228