What is the Greatest Common Factor of 273 and 289?

Greatest common factor (GCF) of 273 and 289 is 1.

GCF(273,289) = 1

We will now calculate the prime factors of 273 and 289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 273 and 289.

How to find the GCF of 273 and 289?

We will first find the prime factorization of 273 and 289. After we will calculate the factors of 273 and 289 and find the biggest common factor number .

Step-1: 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-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 273

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

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

Step-4: Factors of 289

List of positive integer factors of 289 that divides 273 without a remainder.

1, 17

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 273 and 289. The biggest common factor number is the GCF number.
So the greatest common factor 273 and 289 is 1.

Also check out the Least Common Multiple of 273 and 289