What is the Greatest Common Factor of 280 and 289?

Greatest common factor (GCF) of 280 and 289 is 1.

GCF(280,289) = 1

We will now calculate the prime factors of 280 and 289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 280 and 289.

How to find the GCF of 280 and 289?

We will first find the prime factorization of 280 and 289. After we will calculate the factors of 280 and 289 and find the biggest common factor number .

Step-1: Prime Factorization of 280

Prime factors of 280 are 2, 5, 7. Prime factorization of 280 in exponential form is:

280 = 2³ × 5¹ × 7¹

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 280

List of positive integer factors of 280 that divides 280 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140

Step-4: Factors of 289

List of positive integer factors of 289 that divides 280 without a remainder.

1, 17

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 280 and 289. The biggest common factor number is the GCF number.
So the greatest common factor 280 and 289 is 1.

Also check out the Least Common Multiple of 280 and 289