What is the Greatest Common Factor of 1209 and 1215?

Greatest common factor (GCF) of 1209 and 1215 is 3.

GCF(1209,1215) = 3

We will now calculate the prime factors of 1209 and 1215, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1209 and 1215.

How to find the GCF of 1209 and 1215?

We will first find the prime factorization of 1209 and 1215. After we will calculate the factors of 1209 and 1215 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 1215

Prime factors of 1215 are 3, 5. Prime factorization of 1215 in exponential form is:

1215 = 3⁵ × 5¹

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 1215

List of positive integer factors of 1215 that divides 1209 without a remainder.

1, 3, 5, 9, 15, 27, 45, 81, 135, 243, 405

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1209 and 1215. The biggest common factor number is the GCF number.
So the greatest common factor 1209 and 1215 is 3.

Also check out the Least Common Multiple of 1209 and 1215