What is the Greatest Common Factor of 2250 and 2270?

Greatest common factor (GCF) of 2250 and 2270 is 10.

GCF(2250,2270) = 10

We will now calculate the prime factors of 2250 and 2270, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2250 and 2270.

How to find the GCF of 2250 and 2270?

We will first find the prime factorization of 2250 and 2270. After we will calculate the factors of 2250 and 2270 and find the biggest common factor number .

Step-1: Prime Factorization of 2250

Prime factors of 2250 are 2, 3, 5. Prime factorization of 2250 in exponential form is:

2250 = 2¹ × 3² × 5³

Step-2: Prime Factorization of 2270

Prime factors of 2270 are 2, 5, 227. Prime factorization of 2270 in exponential form is:

2270 = 2¹ × 5¹ × 227¹

Step-3: Factors of 2250

List of positive integer factors of 2250 that divides 2250 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 125, 150, 225, 250, 375, 450, 750, 1125

Step-4: Factors of 2270

List of positive integer factors of 2270 that divides 2250 without a remainder.

1, 2, 5, 10, 227, 454, 1135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2250 and 2270. The biggest common factor number is the GCF number.
So the greatest common factor 2250 and 2270 is 10.

Also check out the Least Common Multiple of 2250 and 2270