What is the Greatest Common Factor of 289 and 302?

Greatest common factor (GCF) of 289 and 302 is 1.

GCF(289,302) = 1

We will now calculate the prime factors of 289 and 302, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 289 and 302.

How to find the GCF of 289 and 302?

We will first find the prime factorization of 289 and 302. After we will calculate the factors of 289 and 302 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 302

Prime factors of 302 are 2, 151. Prime factorization of 302 in exponential form is:

302 = 2¹ × 151¹

Step-3: Factors of 289

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

1, 17

Step-4: Factors of 302

List of positive integer factors of 302 that divides 289 without a remainder.

1, 2, 151

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 289 and 302. The biggest common factor number is the GCF number.
So the greatest common factor 289 and 302 is 1.

Also check out the Least Common Multiple of 289 and 302