Greatest Common Factor of 186 and 189

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 186, 189 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 186 and 189 is 3.

GCF(186,189) = 3

GCF of 186 and 189

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

GCF of:
and

Greatest Common Factor of 186 and 189

GCF of 186 and 189 is 3

Prime Factorization of 186


2 186
3 93
31 31
1

Prime factors of 186 are 2,3,31. Prime factorization of 186 in exponential form is:

186 = 21×31×311

Prime Factorization of 189


3 189
3 63
3 21
7 7
1

Prime factors of 189 are 3,7. Prime factorization of 189 in exponential form is:

189 = 33×71

∴ So by taking common prime factors GCF of 186 and 189 is 3

Greatest Common Factor of 186 and 189 by matching factors method

Factors of 186

List of positive integer factors of 186 that divides 186 without a remainder.

1,2,3,6,31,62,93,186

Factors of 189

List of positive integer factors of 189 that divides 189 without a remainder.

1,3,7,9,21,27,63,189

Greatest Common Factor

We found the factors and prime factorization of 186 and 189. The biggest common factor number is the GCF number.
So the greatest common factor 186 and 189 is 3.

Also check out the Least Common Multiple of 186 and 189

Properties of GCF 186 and 189

(i) The GCF of 186 and 189 is associative

GCF of 186 and 189 = GCF of 189 and 186

Related Greatest Common Factor of 186

Related Greatest Common Factor of 189

Frequently Asked Questions on GCF of 186 and 189

1. What is the GCF of 186 and 189?

Answer: GCF of 186 and 189 is 3.

2. What are the Factors of 186?

Answer: Factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186. There are 8 integers that are factors of 186. The greatest factor of 186 is 186.

3. What are the Factors of 189?

Answer: Factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189. There are 8 integers that are factors of 189. The greatest factor of 189 is 189.

4. How to Find the GCF of 186 and 189?

Answer:

Greatest Common Factor of 186 and 189 = 3

Step 1: Find the prime factorization of 186

186 = 2 x 3 x 31

Step 2: Find the prime factorization of 189

189 = 3 x 3 x 3 x 7

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 186 and 189 is 3