What is the Greatest Common Factor of 274 and 289?

Greatest common factor (GCF) of 274 and 289 is 1.

GCF(274,289) = 1

We will now calculate the prime factors of 274 and 289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 274 and 289.

How to find the GCF of 274 and 289?

We will first find the prime factorization of 274 and 289. After we will calculate the factors of 274 and 289 and find the biggest common factor number .

Step-1: Prime Factorization of 274

Prime factors of 274 are 2, 137. Prime factorization of 274 in exponential form is:

274 = 2¹ × 137¹

Step-2: Prime Factorization of 289

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

289 = 17²

Step-3: Factors of 274

List of positive integer factors of 274 that divides 274 without a remainder.

1, 2, 137

Step-4: Factors of 289

List of positive integer factors of 289 that divides 274 without a remainder.

1, 17

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 274 and 289. The biggest common factor number is the GCF number.
So the greatest common factor 274 and 289 is 1.

Also check out the Least Common Multiple of 274 and 289