What is the Greatest Common Factor of 2185 and 2205?

Greatest common factor (GCF) of 2185 and 2205 is 5.

GCF(2185,2205) = 5

We will now calculate the prime factors of 2185 and 2205, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2185 and 2205.

How to find the GCF of 2185 and 2205?

We will first find the prime factorization of 2185 and 2205. After we will calculate the factors of 2185 and 2205 and find the biggest common factor number .

Step-1: Prime Factorization of 2185

Prime factors of 2185 are 5, 19, 23. Prime factorization of 2185 in exponential form is:

2185 = 5¹ × 19¹ × 23¹

Step-2: 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-3: Factors of 2185

List of positive integer factors of 2185 that divides 2185 without a remainder.

1, 5, 19, 23, 95, 115, 437

Step-4: Factors of 2205

List of positive integer factors of 2205 that divides 2185 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2185 and 2205. The biggest common factor number is the GCF number.
So the greatest common factor 2185 and 2205 is 5.

Also check out the Least Common Multiple of 2185 and 2205