What is the Greatest Common Factor of 250 and 260?

Greatest common factor (GCF) of 250 and 260 is 10.

GCF(250,260) = 10

We will now calculate the prime factors of 250 and 260, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 250 and 260.

How to find the GCF of 250 and 260?

We will first find the prime factorization of 250 and 260. After we will calculate the factors of 250 and 260 and find the biggest common factor number .

Step-1: Prime Factorization of 250

Prime factors of 250 are 2, 5. Prime factorization of 250 in exponential form is:

250 = 2¹ × 5³

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 250

List of positive integer factors of 250 that divides 250 without a remainder.

1, 2, 5, 10, 25, 50, 125

Step-4: Factors of 260

List of positive integer factors of 260 that divides 250 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 250 and 260. The biggest common factor number is the GCF number.
So the greatest common factor 250 and 260 is 10.

Also check out the Least Common Multiple of 250 and 260