What is the Greatest Common Factor of 1209 and 1214?

Greatest common factor (GCF) of 1209 and 1214 is 1.

GCF(1209,1214) = 1

We will now calculate the prime factors of 1209 and 1214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1209 and 1214.

How to find the GCF of 1209 and 1214?

We will first find the prime factorization of 1209 and 1214. After we will calculate the factors of 1209 and 1214 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 1214

Prime factors of 1214 are 2, 607. Prime factorization of 1214 in exponential form is:

1214 = 2¹ × 607¹

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 1214

List of positive integer factors of 1214 that divides 1209 without a remainder.

1, 2, 607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1209 and 1214. The biggest common factor number is the GCF number.
So the greatest common factor 1209 and 1214 is 1.

Also check out the Least Common Multiple of 1209 and 1214