What is the Greatest Common Factor of 254 and 272?

Greatest common factor (GCF) of 254 and 272 is 2.

GCF(254,272) = 2

We will now calculate the prime factors of 254 and 272, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 254 and 272.

How to find the GCF of 254 and 272?

We will first find the prime factorization of 254 and 272. After we will calculate the factors of 254 and 272 and find the biggest common factor number .

Step-1: Prime Factorization of 254

Prime factors of 254 are 2, 127. Prime factorization of 254 in exponential form is:

254 = 2¹ × 127¹

Step-2: Prime Factorization of 272

Prime factors of 272 are 2, 17. Prime factorization of 272 in exponential form is:

272 = 2⁴ × 17¹

Step-3: Factors of 254

List of positive integer factors of 254 that divides 254 without a remainder.

1, 2, 127

Step-4: Factors of 272

List of positive integer factors of 272 that divides 254 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 254 and 272. The biggest common factor number is the GCF number.
So the greatest common factor 254 and 272 is 2.

Also check out the Least Common Multiple of 254 and 272