What is the Greatest Common Factor of 1204 and 1214?

Greatest common factor (GCF) of 1204 and 1214 is 2.

GCF(1204,1214) = 2

We will now calculate the prime factors of 1204 and 1214, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1204 and 1214.

How to find the GCF of 1204 and 1214?

We will first find the prime factorization of 1204 and 1214. After we will calculate the factors of 1204 and 1214 and find the biggest common factor number .

Step-1: Prime Factorization of 1204

Prime factors of 1204 are 2, 7, 43. Prime factorization of 1204 in exponential form is:

1204 = 2² × 7¹ × 43¹

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 1204

List of positive integer factors of 1204 that divides 1204 without a remainder.

1, 2, 4, 7, 14, 28, 43, 86, 172, 301, 602

Step-4: Factors of 1214

List of positive integer factors of 1214 that divides 1204 without a remainder.

1, 2, 607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1204 and 1214. The biggest common factor number is the GCF number.
So the greatest common factor 1204 and 1214 is 2.

Also check out the Least Common Multiple of 1204 and 1214