What is the Greatest Common Factor of 259 and 274?

Greatest common factor (GCF) of 259 and 274 is 1.

GCF(259,274) = 1

We will now calculate the prime factors of 259 and 274, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 259 and 274.

How to find the GCF of 259 and 274?

We will first find the prime factorization of 259 and 274. After we will calculate the factors of 259 and 274 and find the biggest common factor number .

Step-1: Prime Factorization of 259

Prime factors of 259 are 7, 37. Prime factorization of 259 in exponential form is:

259 = 7¹ × 37¹

Step-2: Prime Factorization of 274

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

274 = 2¹ × 137¹

Step-3: Factors of 259

List of positive integer factors of 259 that divides 259 without a remainder.

1, 7, 37

Step-4: Factors of 274

List of positive integer factors of 274 that divides 259 without a remainder.

1, 2, 137

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 259 and 274. The biggest common factor number is the GCF number.
So the greatest common factor 259 and 274 is 1.

Also check out the Least Common Multiple of 259 and 274