What is the Greatest Common Factor of 249 and 255?

Greatest common factor (GCF) of 249 and 255 is 3.

GCF(249,255) = 3

We will now calculate the prime factors of 249 and 255, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 249 and 255.

How to find the GCF of 249 and 255?

We will first find the prime factorization of 249 and 255. After we will calculate the factors of 249 and 255 and find the biggest common factor number .

Step-1: Prime Factorization of 249

Prime factors of 249 are 3, 83. Prime factorization of 249 in exponential form is:

249 = 3¹ × 83¹

Step-2: Prime Factorization of 255

Prime factors of 255 are 3, 5, 17. Prime factorization of 255 in exponential form is:

255 = 3¹ × 5¹ × 17¹

Step-3: Factors of 249

List of positive integer factors of 249 that divides 249 without a remainder.

1, 3, 83

Step-4: Factors of 255

List of positive integer factors of 255 that divides 249 without a remainder.

1, 3, 5, 15, 17, 51, 85

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 249 and 255. The biggest common factor number is the GCF number.
So the greatest common factor 249 and 255 is 3.

Also check out the Least Common Multiple of 249 and 255