Greatest Common Factor of 210 and 217

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, 217 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 210 and 217 is 7.

GCF(210,217) = 7

GCF of 210 and 217

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

GCF of:
and

Greatest Common Factor of 210 and 217

GCF of 210 and 217 is 7

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 217


7 217
31 31
1

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

217 = 71×311

∴ So by taking common prime factors GCF of 210 and 217 is 7

Greatest Common Factor of 210 and 217 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 217

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

1,7,31,217

Greatest Common Factor

We found the factors and prime factorization of 210 and 217. The biggest common factor number is the GCF number.
So the greatest common factor 210 and 217 is 7.

Also check out the Least Common Multiple of 210 and 217

Properties of GCF 210 and 217

(i) The GCF of 210 and 217 is associative

GCF of 210 and 217 = GCF of 217 and 210

Related Greatest Common Factor of 210

Related Greatest Common Factor of 217

Frequently Asked Questions on GCF of 210 and 217

1. What is the GCF of 210 and 217?

Answer: GCF of 210 and 217 is 7.

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 217?

Answer: Factors of 217 are 1, 7, 31, 217. There are 4 integers that are factors of 217. The greatest factor of 217 is 217.

4. How to Find the GCF of 210 and 217?

Answer:

Greatest Common Factor of 210 and 217 = 7

Step 1: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 217

217 = 7 x 31

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

GCF = 7

Step 4: Therefore, the greatest common factor of 210 and 217 is 7