What is the Greatest Common Factor of 260 and 265?

Greatest common factor (GCF) of 260 and 265 is 5.

GCF(260,265) = 5

We will now calculate the prime factors of 260 and 265, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 260 and 265.

How to find the GCF of 260 and 265?

We will first find the prime factorization of 260 and 265. After we will calculate the factors of 260 and 265 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 265

Prime factors of 265 are 5, 53. Prime factorization of 265 in exponential form is:

265 = 5¹ × 53¹

Step-3: Factors of 260

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

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

Step-4: Factors of 265

List of positive integer factors of 265 that divides 260 without a remainder.

1, 5, 53

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 260 and 265. The biggest common factor number is the GCF number.
So the greatest common factor 260 and 265 is 5.

Also check out the Least Common Multiple of 260 and 265