What is the Greatest Common Factor of 278 and 289?

Greatest common factor (GCF) of 278 and 289 is 1.

GCF(278,289) = 1

We will now calculate the prime factors of 278 and 289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 278 and 289.

How to find the GCF of 278 and 289?

We will first find the prime factorization of 278 and 289. After we will calculate the factors of 278 and 289 and find the biggest common factor number .

Step-1: Prime Factorization of 278

Prime factors of 278 are 2, 139. Prime factorization of 278 in exponential form is:

278 = 2¹ × 139¹

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 278

List of positive integer factors of 278 that divides 278 without a remainder.

1, 2, 139

Step-4: Factors of 289

List of positive integer factors of 289 that divides 278 without a remainder.

1, 17

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 278 and 289. The biggest common factor number is the GCF number.
So the greatest common factor 278 and 289 is 1.

Also check out the Least Common Multiple of 278 and 289