What is the Greatest Common Factor of 1215 and 1230?

Greatest common factor (GCF) of 1215 and 1230 is 15.

GCF(1215,1230) = 15

We will now calculate the prime factors of 1215 and 1230, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1215 and 1230.

How to find the GCF of 1215 and 1230?

We will first find the prime factorization of 1215 and 1230. After we will calculate the factors of 1215 and 1230 and find the biggest common factor number .

Step-1: Prime Factorization of 1215

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

1215 = 3⁵ × 5¹

Step-2: Prime Factorization of 1230

Prime factors of 1230 are 2, 3, 5, 41. Prime factorization of 1230 in exponential form is:

1230 = 2¹ × 3¹ × 5¹ × 41¹

Step-3: Factors of 1215

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

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

Step-4: Factors of 1230

List of positive integer factors of 1230 that divides 1215 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, 615

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1215 and 1230. The biggest common factor number is the GCF number.
So the greatest common factor 1215 and 1230 is 15.

Also check out the Least Common Multiple of 1215 and 1230