Greatest Common Factor of 210 and 225

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, 225 i.e. 15 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 210 and 225 is 15.

GCF(210,225) = 15

GCF of 210 and 225

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

GCF of:
and

Greatest Common Factor of 210 and 225

GCF of 210 and 225 is 15

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 225


3 225
3 75
5 25
5 5
1

Prime factors of 225 are 3,5. Prime factorization of 225 in exponential form is:

225 = 32×52

∴ So by taking common prime factors GCF of 210 and 225 is 15

Greatest Common Factor of 210 and 225 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 225

List of positive integer factors of 225 that divides 225 without a remainder.

1,3,5,9,15,25,45,75,225

Greatest Common Factor

We found the factors and prime factorization of 210 and 225. The biggest common factor number is the GCF number.
So the greatest common factor 210 and 225 is 15.

Also check out the Least Common Multiple of 210 and 225

Properties of GCF 210 and 225

(i) The GCF of 210 and 225 is associative

GCF of 210 and 225 = GCF of 225 and 210

Related Greatest Common Factor of 210

Related Greatest Common Factor of 225

Frequently Asked Questions on GCF of 210 and 225

1. What is the GCF of 210 and 225?

Answer: GCF of 210 and 225 is 15.

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 225?

Answer: Factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225. There are 9 integers that are factors of 225. The greatest factor of 225 is 225.

4. How to Find the GCF of 210 and 225?

Answer:

Greatest Common Factor of 210 and 225 = 15

Step 1: Find the prime factorization of 210

210 = 2 x 3 x 5 x 7

Step 2: Find the prime factorization of 225

225 = 3 x 3 x 5 x 5

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

GCF = 3 x 5 = 15

Step 4: Therefore, the greatest common factor of 210 and 225 is 15