What is the Greatest Common Factor of 208 and 216?

Greatest common factor (GCF) of 208 and 216 is 8.

GCF(208,216) = 8

We will now calculate the prime factors of 208 and 216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 208 and 216.

How to find the GCF of 208 and 216?

We will first find the prime factorization of 208 and 216. After we will calculate the factors of 208 and 216 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 216

Prime factors of 216 are 2, 3. Prime factorization of 216 in exponential form is:

216 = 2³ × 3³

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 216

List of positive integer factors of 216 that divides 208 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 208 and 216. The biggest common factor number is the GCF number.
So the greatest common factor 208 and 216 is 8.

Also check out the Least Common Multiple of 208 and 216