What is the Greatest Common Factor of 214 and 219?

Greatest common factor (GCF) of 214 and 219 is 1.

GCF(214,219) = 1

We will now calculate the prime factors of 214 and 219, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 214 and 219.

How to find the GCF of 214 and 219?

We will first find the prime factorization of 214 and 219. After we will calculate the factors of 214 and 219 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 219

Prime factors of 219 are 3, 73. Prime factorization of 219 in exponential form is:

219 = 3¹ × 73¹

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 219

List of positive integer factors of 219 that divides 214 without a remainder.

1, 3, 73

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 214 and 219. The biggest common factor number is the GCF number.
So the greatest common factor 214 and 219 is 1.

Also check out the Least Common Multiple of 214 and 219