What is the Greatest Common Factor of 2205 and 2225?

Greatest common factor (GCF) of 2205 and 2225 is 5.

GCF(2205,2225) = 5

We will now calculate the prime factors of 2205 and 2225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2205 and 2225.

How to find the GCF of 2205 and 2225?

We will first find the prime factorization of 2205 and 2225. After we will calculate the factors of 2205 and 2225 and find the biggest common factor number .

Step-1: Prime Factorization of 2205

Prime factors of 2205 are 3, 5, 7. Prime factorization of 2205 in exponential form is:

2205 = 3² × 5¹ × 7²

Step-2: Prime Factorization of 2225

Prime factors of 2225 are 5, 89. Prime factorization of 2225 in exponential form is:

2225 = 5² × 89¹

Step-3: Factors of 2205

List of positive integer factors of 2205 that divides 2205 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735

Step-4: Factors of 2225

List of positive integer factors of 2225 that divides 2205 without a remainder.

1, 5, 25, 89, 445

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2205 and 2225. The biggest common factor number is the GCF number.
So the greatest common factor 2205 and 2225 is 5.

Also check out the Least Common Multiple of 2205 and 2225