What is the Greatest Common Factor of 275 and 288?

Greatest common factor (GCF) of 275 and 288 is 1.

GCF(275,288) = 1

We will now calculate the prime factors of 275 and 288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 275 and 288.

How to find the GCF of 275 and 288?

We will first find the prime factorization of 275 and 288. After we will calculate the factors of 275 and 288 and find the biggest common factor number .

Step-1: Prime Factorization of 275

Prime factors of 275 are 5, 11. Prime factorization of 275 in exponential form is:

275 = 5² × 11¹

Step-2: Prime Factorization of 288

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

288 = 2⁵ × 3²

Step-3: Factors of 275

List of positive integer factors of 275 that divides 275 without a remainder.

1, 5, 11, 25, 55

Step-4: Factors of 288

List of positive integer factors of 288 that divides 275 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 275 and 288. The biggest common factor number is the GCF number.
So the greatest common factor 275 and 288 is 1.

Also check out the Least Common Multiple of 275 and 288