GCD of 27, 9, 75, 84 Calculator

Given Input numbers are 27, 9, 75, 84

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

Divisors of 27

List of positive integer divisors of 27 that divides 27 without a remainder.

1, 3, 9, 27

Divisors of 9

List of positive integer divisors of 9 that divides 9 without a remainder.

1, 3, 9

Divisors of 75

List of positive integer divisors of 75 that divides 75 without a remainder.

1, 3, 5, 15, 25, 75

Divisors of 84

List of positive integer divisors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Greatest Common Divisior

We found the divisors of 27, 9, 75, 84 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 27, 9, 75, 84 is 3.

Therefore, GCD of numbers 27, 9, 75, 84 is 3

Given Input Data is 27, 9, 75, 84

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

Prime Factorization of 27 is 3 x 3 x 3

Prime Factorization of 9 is 3 x 3

Prime Factorization of 75 is 3 x 5 x 5

Prime Factorization of 84 is 2 x 2 x 3 x 7

Highest common occurrences in the given inputs are 3¹

Multiplying them we get the GCD as 3

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(27, 9) = 27

GCD(27, 9) = ( 27 x 9 ) / 27

GCD(27, 9) = 243 / 27

GCD(27, 9) = 9

Step2:

Here we consider the GCD from the above i.e. 9 as first number and the next as 75

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

LCM(9, 75) = 225

GCD(9, 75) = ( 9 x 75 ) / 225

GCD(9, 75) = 675 / 225

GCD(9, 75) = 3

Step3:

Here we consider the GCD from the above i.e. 3 as first number and the next as 84

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

LCM(3, 84) = 84

GCD(3, 84) = ( 3 x 84 ) / 84

GCD(3, 84) = 252 / 84

GCD(3, 84) = 3

GCD of 27, 9, 75, 84 is 3

Here are some samples of GCD of Numbers calculations.

• GCD of 24, 9, 10, 86
• GCD of 57, 1, 14, 18
• GCD of 90, 5, 42, 97
• GCD of 65, 3, 69, 80
• GCD of 98, 9, 65, 46

1. What is the GCD of 27, 9, 75, 84?

GCD of 27, 9, 75, 84 is 3

2. Where do I get the detailed procedure to find GCD of 27, 9, 75, 84?

You can find a detailed procedure to find GCD of 27, 9, 75, 84 on our page.

3. How to find GCD of 27, 9, 75, 84 on a calculator?

You can find the GCD of 27, 9, 75, 84 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.