What is the Greatest Common Factor of 2205 and 2219?

Greatest common factor (GCF) of 2205 and 2219 is 7.

GCF(2205,2219) = 7

We will now calculate the prime factors of 2205 and 2219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2205 and 2219.

How to find the GCF of 2205 and 2219?

We will first find the prime factorization of 2205 and 2219. After we will calculate the factors of 2205 and 2219 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 2219

Prime factors of 2219 are 7, 317. Prime factorization of 2219 in exponential form is:

2219 = 7¹ × 317¹

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 2219

List of positive integer factors of 2219 that divides 2205 without a remainder.

1, 7, 317

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2205 and 2219. The biggest common factor number is the GCF number.
So the greatest common factor 2205 and 2219 is 7.

Also check out the Least Common Multiple of 2205 and 2219