What is the Greatest Common Factor of 2197 and 2208?

Greatest common factor (GCF) of 2197 and 2208 is 1.

GCF(2197,2208) = 1

We will now calculate the prime factors of 2197 and 2208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2197 and 2208.

How to find the GCF of 2197 and 2208?

We will first find the prime factorization of 2197 and 2208. After we will calculate the factors of 2197 and 2208 and find the biggest common factor number .

Step-1: Prime Factorization of 2197

Prime factors of 2197 are 13. Prime factorization of 2197 in exponential form is:

2197 = 13³

Step-2: 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-3: Factors of 2197

List of positive integer factors of 2197 that divides 2197 without a remainder.

1, 13, 169

Step-4: Factors of 2208

List of positive integer factors of 2208 that divides 2197 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2197 and 2208. The biggest common factor number is the GCF number.
So the greatest common factor 2197 and 2208 is 1.

Also check out the Least Common Multiple of 2197 and 2208