Where do I get the detailed procedure to find GCD of 189, 345, 180?

You can find a detailed procedure to find GCD of 189, 345, 180 on our page.

How to find GCD of 189, 345, 180 on a calculator?

You can find the GCD of 189, 345, 180 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.

GCD of 189, 345, 180 Calculator

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Online GCD Calculator is useful to find the GCD of 189, 345, 180 quickly. Get the easiest ways to solve the greatest common divisor of 189, 345, 180 i.e 3 in different methods as follows.

How to Find GCD of Numbers 189, 345, 180 with Factoring?

Given Input numbers are 189, 345, 180

In the factoring method, we have to find the divisors of all numbers

Divisors of 189 :

The positive integer divisors of 189 that completely divides 189 are.

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

Divisors of 345 :

The positive integer divisors of 345 that completely divides 345 are.

1, 3, 5, 15, 23, 69, 115, 345

Divisors of 180 :

The positive integer divisors of 180 that completely divides 180 are.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

GCD of numbers is the greatest common divisor

So, the GCD (189, 345, 180) = 3.

Find GCD of 189, 345, 180 using Prime Factorization

Given numbers are 189, 345, 180

The list of prime factors of all numbers are

Prime factors of 189 are 3 x 3 x 3 x 7

Prime factors of 345 are 3 x 5 x 23

Prime factors of 180 are 2 x 2 x 3 x 3 x 5

The highest common occurrence is 3¹

Therefore, GCD of 189, 345, 180 is 3.

Steps to Calculate GCD of 189, 345, 180 using LCM Formula

Given numbers are 189, 345, 180

GCD of 2 numbers formula is GCD(a, b) = ( a x b) / LCM(a, b)

Apply this formula for all numbers.

Step1:

LCM(189, 345) = 21735

GCD(189, 345) = ( 189 x 345 ) / 21735

= 189 / 345

= 189

Step2:

LCM(3, 180) = 180

GCD(3, 180) = ( 3 x 180 ) / 180

= 3 / 180

= 3

So, Greatest Common Divisor of 189, 345, 180 is 3

GCD of Numbers Calculation Examples

Here are some samples of GCD of Numbers calculations.

Greatest Common Divisor of 189, 345, 180

Given numbers are 189, 345, 180
The greatest common divisor of numbers 189, 345, 180 can be found in various methods such as the LCM formula, factoring, and prime factorization. The GCD of numbers 189, 345, 180 is 3.

FAQs on GCD of 189, 345, 180 Calculator

1. What is the GCD of 189, 345, 180?

GCD of given numbers 189, 345, 180 is 3

2. How to calculate the greatest common divisor of 189, 345, 180?

We can find the highest common divisor of 189, 345, 180 easily using the prime factorization method. Just list the prime factors of all numbers and pick the highest common factor which is the GCD of 189, 345, 180 i.e 3.

3. How can I use the GCD of 189, 345, 180Calculator?

Out the numbers 189, 345, 180 into the GCD calculator and hit the calculate button to get the greatest common divisor as result.