What is the Greatest Common Factor of 189 and 208?

Greatest common factor (GCF) of 189 and 208 is 1.

GCF(189,208) = 1

We will now calculate the prime factors of 189 and 208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 189 and 208.

How to find the GCF of 189 and 208?

We will first find the prime factorization of 189 and 208. After we will calculate the factors of 189 and 208 and find the biggest common factor number .

Step-1: Prime Factorization of 189

Prime factors of 189 are 3, 7. Prime factorization of 189 in exponential form is:

189 = 3³ × 7¹

Step-2: Prime Factorization of 208

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

208 = 2⁴ × 13¹

Step-3: Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1, 3, 7, 9, 21, 27, 63

Step-4: Factors of 208

List of positive integer factors of 208 that divides 189 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 189 and 208. The biggest common factor number is the GCF number.
So the greatest common factor 189 and 208 is 1.

Also check out the Least Common Multiple of 189 and 208