What is the Greatest Common Factor of 274 and 288?

Greatest common factor (GCF) of 274 and 288 is 2.

GCF(274,288) = 2

We will now calculate the prime factors of 274 and 288, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 274 and 288.

How to find the GCF of 274 and 288?

We will first find the prime factorization of 274 and 288. After we will calculate the factors of 274 and 288 and find the biggest common factor number .

Step-1: Prime Factorization of 274

Prime factors of 274 are 2, 137. Prime factorization of 274 in exponential form is:

274 = 2¹ × 137¹

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 274

List of positive integer factors of 274 that divides 274 without a remainder.

1, 2, 137

Step-4: Factors of 288

List of positive integer factors of 288 that divides 274 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 274 and 288. The biggest common factor number is the GCF number.
So the greatest common factor 274 and 288 is 2.

Also check out the Least Common Multiple of 274 and 288