What is the Greatest Common Factor of 259 and 273?

Greatest common factor (GCF) of 259 and 273 is 7.

GCF(259,273) = 7

We will now calculate the prime factors of 259 and 273, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 259 and 273.

How to find the GCF of 259 and 273?

We will first find the prime factorization of 259 and 273. After we will calculate the factors of 259 and 273 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 273

Prime factors of 273 are 3, 7, 13. Prime factorization of 273 in exponential form is:

273 = 3¹ × 7¹ × 13¹

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 273

List of positive integer factors of 273 that divides 259 without a remainder.

1, 3, 7, 13, 21, 39, 91

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 259 and 273. The biggest common factor number is the GCF number.
So the greatest common factor 259 and 273 is 7.

Also check out the Least Common Multiple of 259 and 273