What is the Greatest Common Factor of 259 and 272?

Greatest common factor (GCF) of 259 and 272 is 1.

GCF(259,272) = 1

We will now calculate the prime factors of 259 and 272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 259 and 272.

How to find the GCF of 259 and 272?

We will first find the prime factorization of 259 and 272. After we will calculate the factors of 259 and 272 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 272

Prime factors of 272 are 2, 17. Prime factorization of 272 in exponential form is:

272 = 2⁴ × 17¹

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 272

List of positive integer factors of 272 that divides 259 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 259 and 272. The biggest common factor number is the GCF number.
So the greatest common factor 259 and 272 is 1.

Also check out the Least Common Multiple of 259 and 272