What is the Greatest Common Factor of 208 and 217?

Greatest common factor (GCF) of 208 and 217 is 1.

GCF(208,217) = 1

We will now calculate the prime factors of 208 and 217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 208 and 217.

How to find the GCF of 208 and 217?

We will first find the prime factorization of 208 and 217. After we will calculate the factors of 208 and 217 and find the biggest common factor number .

Step-1: Prime Factorization of 208

Prime factors of 208 are 2, 13. Prime factorization of 208 in exponential form is:

208 = 2⁴ × 13¹

Step-2: Prime Factorization of 217

Prime factors of 217 are 7, 31. Prime factorization of 217 in exponential form is:

217 = 7¹ × 31¹

Step-3: Factors of 208

List of positive integer factors of 208 that divides 208 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104

Step-4: Factors of 217

List of positive integer factors of 217 that divides 208 without a remainder.

1, 7, 31

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 208 and 217. The biggest common factor number is the GCF number.
So the greatest common factor 208 and 217 is 1.

Also check out the Least Common Multiple of 208 and 217