GCD of 120, 208, 189, 789 Calculator

Given Input numbers are 120, 208, 189, 789

To find the GCD of numbers using factoring list out all the divisors of each number

Divisors of 120

List of positive integer divisors of 120 that divides 120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Divisors of 208

List of positive integer divisors of 208 that divides 208 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 104, 208

Divisors of 189

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

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

Divisors of 789

List of positive integer divisors of 789 that divides 789 without a remainder.

1, 3, 263, 789

Greatest Common Divisior

We found the divisors of 120, 208, 189, 789 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 120, 208, 189, 789 is 1.

Therefore, GCD of numbers 120, 208, 189, 789 is 1

Given Input Data is 120, 208, 189, 789

Make a list of Prime Factors of all the given numbers initially

Prime Factorization of 120 is 2 x 2 x 2 x 3 x 5

Prime Factorization of 208 is 2 x 2 x 2 x 2 x 13

Prime Factorization of 189 is 3 x 3 x 3 x 7

Prime Factorization of 789 is 3 x 263

The above numbers do not have any common prime factor. So GCD is 1

Step1:

Let's calculate the GCD of first two numbers

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

LCM(120, 208) = 3120

GCD(120, 208) = ( 120 x 208 ) / 3120

GCD(120, 208) = 24960 / 3120

GCD(120, 208) = 8

Step2:

Here we consider the GCD from the above i.e. 8 as first number and the next as 189

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

LCM(8, 189) = 1512

GCD(8, 189) = ( 8 x 189 ) / 1512

GCD(8, 189) = 1512 / 1512

GCD(8, 189) = 1

Step3:

Here we consider the GCD from the above i.e. 1 as first number and the next as 789

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

LCM(1, 789) = 789

GCD(1, 789) = ( 1 x 789 ) / 789

GCD(1, 789) = 789 / 789

GCD(1, 789) = 1

GCD of 120, 208, 189, 789 is 1

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1. What is the GCD of 120, 208, 189, 789?

GCD of 120, 208, 189, 789 is 1

2. Where do I get the detailed procedure to find GCD of 120, 208, 189, 789?

You can find a detailed procedure to find GCD of 120, 208, 189, 789 on our page.

3. How to find GCD of 120, 208, 189, 789 on a calculator?

You can find the GCD of 120, 208, 189, 789 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.