What is the Greatest Common Factor of 289 and 308?

Greatest common factor (GCF) of 289 and 308 is 1.

GCF(289,308) = 1

We will now calculate the prime factors of 289 and 308, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 289 and 308.

How to find the GCF of 289 and 308?

We will first find the prime factorization of 289 and 308. After we will calculate the factors of 289 and 308 and find the biggest common factor number .

Step-1: Prime Factorization of 289

Prime factors of 289 are 17. Prime factorization of 289 in exponential form is:

289 = 17²

Step-2: Prime Factorization of 308

Prime factors of 308 are 2, 7, 11. Prime factorization of 308 in exponential form is:

308 = 2² × 7¹ × 11¹

Step-3: Factors of 289

List of positive integer factors of 289 that divides 289 without a remainder.

1, 17

Step-4: Factors of 308

List of positive integer factors of 308 that divides 289 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 289 and 308. The biggest common factor number is the GCF number.
So the greatest common factor 289 and 308 is 1.

Also check out the Least Common Multiple of 289 and 308