What is the Greatest Common Factor of 260 and 275?

Greatest common factor (GCF) of 260 and 275 is 5.

GCF(260,275) = 5

We will now calculate the prime factors of 260 and 275, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 260 and 275.

How to find the GCF of 260 and 275?

We will first find the prime factorization of 260 and 275. After we will calculate the factors of 260 and 275 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 275

Prime factors of 275 are 5, 11. Prime factorization of 275 in exponential form is:

275 = 5² × 11¹

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 275

List of positive integer factors of 275 that divides 260 without a remainder.

1, 5, 11, 25, 55

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 260 and 275. The biggest common factor number is the GCF number.
So the greatest common factor 260 and 275 is 5.

Also check out the Least Common Multiple of 260 and 275