What is the Greatest Common Factor of 213 and 222?

Greatest common factor (GCF) of 213 and 222 is 3.

GCF(213,222) = 3

We will now calculate the prime factors of 213 and 222, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 213 and 222.

How to find the GCF of 213 and 222?

We will first find the prime factorization of 213 and 222. After we will calculate the factors of 213 and 222 and find the biggest common factor number .

Step-1: Prime Factorization of 213

Prime factors of 213 are 3, 71. Prime factorization of 213 in exponential form is:

213 = 3¹ × 71¹

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 213

List of positive integer factors of 213 that divides 213 without a remainder.

1, 3, 71

Step-4: Factors of 222

List of positive integer factors of 222 that divides 213 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 213 and 222. The biggest common factor number is the GCF number.
So the greatest common factor 213 and 222 is 3.

Also check out the Least Common Multiple of 213 and 222