Greatest Common Factor of 214 and 222

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 214, 222 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 214 and 222 is 2.

GCF(214,222) = 2

GCF of 214 and 222

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 214 and 222

GCF of 214 and 222 is 2

Prime Factorization of 214


2 214
107 107
1

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

214 = 21×1071

Prime Factorization of 222


2 222
3 111
37 37
1

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

222 = 21×31×371

∴ So by taking common prime factors GCF of 214 and 222 is 2

Greatest Common Factor of 214 and 222 by matching factors method

Factors of 214

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

1,2,107,214

Factors of 222

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

1,2,3,6,37,74,111,222

Greatest Common Factor

We found the factors and prime factorization of 214 and 222. The biggest common factor number is the GCF number.
So the greatest common factor 214 and 222 is 2.

Also check out the Least Common Multiple of 214 and 222

Properties of GCF 214 and 222

(i) The GCF of 214 and 222 is associative

GCF of 214 and 222 = GCF of 222 and 214

Related Greatest Common Factor of 214

Related Greatest Common Factor of 222

Frequently Asked Questions on GCF of 214 and 222

1. What is the GCF of 214 and 222?

Answer: GCF of 214 and 222 is 2.

2. What are the Factors of 214?

Answer: Factors of 214 are 1, 2, 107, 214. There are 4 integers that are factors of 214. The greatest factor of 214 is 214.

3. What are the Factors of 222?

Answer: Factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222. There are 8 integers that are factors of 222. The greatest factor of 222 is 222.

4. How to Find the GCF of 214 and 222?

Answer:

Greatest Common Factor of 214 and 222 = 2

Step 1: Find the prime factorization of 214

214 = 2 x 107

Step 2: Find the prime factorization of 222

222 = 2 x 3 x 37

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2

Step 4: Therefore, the greatest common factor of 214 and 222 is 2