What is the Greatest Common Factor of 1205 and 1209?

Greatest common factor (GCF) of 1205 and 1209 is 1.

GCF(1205,1209) = 1

We will now calculate the prime factors of 1205 and 1209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1205 and 1209.

How to find the GCF of 1205 and 1209?

We will first find the prime factorization of 1205 and 1209. After we will calculate the factors of 1205 and 1209 and find the biggest common factor number .

Step-1: Prime Factorization of 1205

Prime factors of 1205 are 5, 241. Prime factorization of 1205 in exponential form is:

1205 = 5¹ × 241¹

Step-2: Prime Factorization of 1209

Prime factors of 1209 are 3, 13, 31. Prime factorization of 1209 in exponential form is:

1209 = 3¹ × 13¹ × 31¹

Step-3: Factors of 1205

List of positive integer factors of 1205 that divides 1205 without a remainder.

1, 5, 241

Step-4: Factors of 1209

List of positive integer factors of 1209 that divides 1205 without a remainder.

1, 3, 13, 31, 39, 93, 403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1205 and 1209. The biggest common factor number is the GCF number.
So the greatest common factor 1205 and 1209 is 1.

Also check out the Least Common Multiple of 1205 and 1209