What is the Greatest Common Factor of 254 and 260?

Greatest common factor (GCF) of 254 and 260 is 2.

GCF(254,260) = 2

We will now calculate the prime factors of 254 and 260, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 254 and 260.

How to find the GCF of 254 and 260?

We will first find the prime factorization of 254 and 260. After we will calculate the factors of 254 and 260 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 260

Prime factors of 260 are 2, 5, 13. Prime factorization of 260 in exponential form is:

260 = 2² × 5¹ × 13¹

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 260

List of positive integer factors of 260 that divides 254 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 254 and 260. The biggest common factor number is the GCF number.
So the greatest common factor 254 and 260 is 2.

Also check out the Least Common Multiple of 254 and 260