What is the Greatest Common Factor of 217 and 222?

Greatest common factor (GCF) of 217 and 222 is 1.

GCF(217,222) = 1

We will now calculate the prime factors of 217 and 222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 217 and 222.

How to find the GCF of 217 and 222?

We will first find the prime factorization of 217 and 222. After we will calculate the factors of 217 and 222 and find the biggest common factor number .

Step-1: Prime Factorization of 217

Prime factors of 217 are 7, 31. Prime factorization of 217 in exponential form is:

217 = 7¹ × 31¹

Step-2: Prime Factorization of 222

Prime factors of 222 are 2, 3, 37. Prime factorization of 222 in exponential form is:

222 = 2¹ × 3¹ × 37¹

Step-3: Factors of 217

List of positive integer factors of 217 that divides 217 without a remainder.

1, 7, 31

Step-4: Factors of 222

List of positive integer factors of 222 that divides 217 without a remainder.

1, 2, 3, 6, 37, 74, 111

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 217 and 222. The biggest common factor number is the GCF number.
So the greatest common factor 217 and 222 is 1.

Also check out the Least Common Multiple of 217 and 222