Greatest Common Factor of 210 and 213

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, 213 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 210 and 213 is 3.

GCF(210,213) = 3

GCF of 210 and 213

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

GCF of:
and

Greatest Common Factor of 210 and 213

GCF of 210 and 213 is 3

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 213


3 213
71 71
1

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

213 = 31×711

∴ So by taking common prime factors GCF of 210 and 213 is 3

Greatest Common Factor of 210 and 213 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 213

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

1,3,71,213

Greatest Common Factor

We found the factors and prime factorization of 210 and 213. The biggest common factor number is the GCF number.
So the greatest common factor 210 and 213 is 3.

Also check out the Least Common Multiple of 210 and 213

Properties of GCF 210 and 213

(i) The GCF of 210 and 213 is associative

GCF of 210 and 213 = GCF of 213 and 210

Related Greatest Common Factor of 210

Related Greatest Common Factor of 213

Frequently Asked Questions on GCF of 210 and 213

1. What is the GCF of 210 and 213?

Answer: GCF of 210 and 213 is 3.

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 213?

Answer: Factors of 213 are 1, 3, 71, 213. There are 4 integers that are factors of 213. The greatest factor of 213 is 213.

4. How to Find the GCF of 210 and 213?

Answer:

Greatest Common Factor of 210 and 213 = 3

Step 1: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 213

213 = 3 x 71

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

GCF = 3

Step 4: Therefore, the greatest common factor of 210 and 213 is 3