What is the Greatest Common Factor of 2275 and 2289?

Greatest common factor (GCF) of 2275 and 2289 is 7.

GCF(2275,2289) = 7

We will now calculate the prime factors of 2275 and 2289, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2275 and 2289.

How to find the GCF of 2275 and 2289?

We will first find the prime factorization of 2275 and 2289. After we will calculate the factors of 2275 and 2289 and find the biggest common factor number .

Step-1: Prime Factorization of 2275

Prime factors of 2275 are 5, 7, 13. Prime factorization of 2275 in exponential form is:

2275 = 5² × 7¹ × 13¹

Step-2: Prime Factorization of 2289

Prime factors of 2289 are 3, 7, 109. Prime factorization of 2289 in exponential form is:

2289 = 3¹ × 7¹ × 109¹

Step-3: Factors of 2275

List of positive integer factors of 2275 that divides 2275 without a remainder.

1, 5, 7, 13, 25, 35, 65, 91, 175, 325, 455

Step-4: Factors of 2289

List of positive integer factors of 2289 that divides 2275 without a remainder.

1, 3, 7, 21, 109, 327, 763

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2275 and 2289. The biggest common factor number is the GCF number.
So the greatest common factor 2275 and 2289 is 7.

Also check out the Least Common Multiple of 2275 and 2289