What is the Greatest Common Factor of 289 and 300?

Greatest common factor (GCF) of 289 and 300 is 1.

GCF(289,300) = 1

We will now calculate the prime factors of 289 and 300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 289 and 300.

How to find the GCF of 289 and 300?

We will first find the prime factorization of 289 and 300. After we will calculate the factors of 289 and 300 and find the biggest common factor number .

Step-1: Prime Factorization of 289

Prime factors of 289 are 17. Prime factorization of 289 in exponential form is:

289 = 17²

Step-2: Prime Factorization of 300

Prime factors of 300 are 2, 3, 5. Prime factorization of 300 in exponential form is:

300 = 2² × 3¹ × 5²

Step-3: Factors of 289

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

1, 17

Step-4: Factors of 300

List of positive integer factors of 300 that divides 289 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 289 and 300. The biggest common factor number is the GCF number.
So the greatest common factor 289 and 300 is 1.

Also check out the Least Common Multiple of 289 and 300