What is the Greatest Common Factor of 1209 and 1228?

Greatest common factor (GCF) of 1209 and 1228 is 1.

GCF(1209,1228) = 1

We will now calculate the prime factors of 1209 and 1228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1209 and 1228.

How to find the GCF of 1209 and 1228?

We will first find the prime factorization of 1209 and 1228. After we will calculate the factors of 1209 and 1228 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1228

Prime factors of 1228 are 2, 307. Prime factorization of 1228 in exponential form is:

1228 = 2² × 307¹

Step-3: Factors of 1209

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

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

Step-4: Factors of 1228

List of positive integer factors of 1228 that divides 1209 without a remainder.

1, 2, 4, 307, 614

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1209 and 1228. The biggest common factor number is the GCF number.
So the greatest common factor 1209 and 1228 is 1.

Also check out the Least Common Multiple of 1209 and 1228