What is the Greatest Common Factor of 259 and 266?

Greatest common factor (GCF) of 259 and 266 is 7.

GCF(259,266) = 7

We will now calculate the prime factors of 259 and 266, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 259 and 266.

How to find the GCF of 259 and 266?

We will first find the prime factorization of 259 and 266. After we will calculate the factors of 259 and 266 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 266

Prime factors of 266 are 2, 7, 19. Prime factorization of 266 in exponential form is:

266 = 2¹ × 7¹ × 19¹

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 266

List of positive integer factors of 266 that divides 259 without a remainder.

1, 2, 7, 14, 19, 38, 133

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 259 and 266. The biggest common factor number is the GCF number.
So the greatest common factor 259 and 266 is 7.

Also check out the Least Common Multiple of 259 and 266