Greatest Common Factor of 210 and 214

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 210, 214 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 210 and 214 is 2.

GCF(210,214) = 2

GCF of 210 and 214

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

GCF of:
and

Greatest Common Factor of 210 and 214

GCF of 210 and 214 is 2

Prime Factorization of 210


2 210
3 105
5 35
7 7
1

Prime factors of 210 are 2,3,5,7. Prime factorization of 210 in exponential form is:

210 = 21×31×51×71

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

∴ So by taking common prime factors GCF of 210 and 214 is 2

Greatest Common Factor of 210 and 214 by matching factors method

Factors of 210

List of positive integer factors of 210 that divides 210 without a remainder.

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Factors of 214

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

1,2,107,214

Greatest Common Factor

We found the factors and prime factorization of 210 and 214. The biggest common factor number is the GCF number.
So the greatest common factor 210 and 214 is 2.

Also check out the Least Common Multiple of 210 and 214

Properties of GCF 210 and 214

(i) The GCF of 210 and 214 is associative

GCF of 210 and 214 = GCF of 214 and 210

Related Greatest Common Factor of 210

Related Greatest Common Factor of 214

Frequently Asked Questions on GCF of 210 and 214

1. What is the GCF of 210 and 214?

Answer: GCF of 210 and 214 is 2.

2. What are the Factors of 210?

Answer: Factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. There are 16 integers that are factors of 210. The greatest factor of 210 is 210.

3. 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.

4. How to Find the GCF of 210 and 214?

Answer:

Greatest Common Factor of 210 and 214 = 2

Step 1: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 214

214 = 2 x 107

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 210 and 214 is 2