What is the Greatest Common Factor of 288 and 305?

Greatest common factor (GCF) of 288 and 305 is 1.

GCF(288,305) = 1

We will now calculate the prime factors of 288 and 305, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 288 and 305.

How to find the GCF of 288 and 305?

We will first find the prime factorization of 288 and 305. After we will calculate the factors of 288 and 305 and find the biggest common factor number .

Step-1: Prime Factorization of 288

Prime factors of 288 are 2, 3. Prime factorization of 288 in exponential form is:

288 = 2⁵ × 3²

Step-2: Prime Factorization of 305

Prime factors of 305 are 5, 61. Prime factorization of 305 in exponential form is:

305 = 5¹ × 61¹

Step-3: Factors of 288

List of positive integer factors of 288 that divides 288 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144

Step-4: Factors of 305

List of positive integer factors of 305 that divides 288 without a remainder.

1, 5, 61

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 288 and 305. The biggest common factor number is the GCF number.
So the greatest common factor 288 and 305 is 1.

Also check out the Least Common Multiple of 288 and 305