What is the Greatest Common Factor of 214 and 230?

Greatest common factor (GCF) of 214 and 230 is 2.

GCF(214,230) = 2

We will now calculate the prime factors of 214 and 230, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 214 and 230.

How to find the GCF of 214 and 230?

We will first find the prime factorization of 214 and 230. After we will calculate the factors of 214 and 230 and find the biggest common factor number .

Step-1: Prime Factorization of 214

Prime factors of 214 are 2, 107. Prime factorization of 214 in exponential form is:

214 = 2¹ × 107¹

Step-2: Prime Factorization of 230

Prime factors of 230 are 2, 5, 23. Prime factorization of 230 in exponential form is:

230 = 2¹ × 5¹ × 23¹

Step-3: Factors of 214

List of positive integer factors of 214 that divides 214 without a remainder.

1, 2, 107

Step-4: Factors of 230

List of positive integer factors of 230 that divides 214 without a remainder.

1, 2, 5, 10, 23, 46, 115

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 214 and 230. The biggest common factor number is the GCF number.
So the greatest common factor 214 and 230 is 2.

Also check out the Least Common Multiple of 214 and 230