What is the Greatest Common Factor of 1214 and 1230?

Greatest common factor (GCF) of 1214 and 1230 is 2.

GCF(1214,1230) = 2

We will now calculate the prime factors of 1214 and 1230, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1214 and 1230.

How to find the GCF of 1214 and 1230?

We will first find the prime factorization of 1214 and 1230. After we will calculate the factors of 1214 and 1230 and find the biggest common factor number .

Step-1: Prime Factorization of 1214

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

1214 = 2¹ × 607¹

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 1214

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

1, 2, 607

Step-4: Factors of 1230

List of positive integer factors of 1230 that divides 1214 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 1214 and 1230. The biggest common factor number is the GCF number.
So the greatest common factor 1214 and 1230 is 2.

Also check out the Least Common Multiple of 1214 and 1230