GCD of 585, 414, 996 Calculator

Given Input numbers are 585, 414, 996

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

Divisors of 585

List of positive integer divisors of 585 that divides 585 without a remainder.

1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585

Divisors of 414

List of positive integer divisors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

Divisors of 996

List of positive integer divisors of 996 that divides 996 without a remainder.

1, 2, 3, 4, 6, 12, 83, 166, 249, 332, 498, 996

Greatest Common Divisior

We found the divisors of 585, 414, 996 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 585, 414, 996 is 3.

Therefore, GCD of numbers 585, 414, 996 is 3

Given Input Data is 585, 414, 996

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

Prime Factorization of 585 is 3 x 3 x 5 x 13

Prime Factorization of 414 is 2 x 3 x 3 x 23

Prime Factorization of 996 is 2 x 2 x 3 x 83

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(585, 414) = 26910

GCD(585, 414) = ( 585 x 414 ) / 26910

GCD(585, 414) = 242190 / 26910

GCD(585, 414) = 9

Step2:

Here we consider the GCD from the above i.e. 9 as first number and the next as 996

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

LCM(9, 996) = 2988

GCD(9, 996) = ( 9 x 996 ) / 2988

GCD(9, 996) = 8964 / 2988

GCD(9, 996) = 3

GCD of 585, 414, 996 is 3

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1. What is the GCD of 585, 414, 996?

GCD of 585, 414, 996 is 3

2. Where do I get the detailed procedure to find GCD of 585, 414, 996?

You can find a detailed procedure to find GCD of 585, 414, 996 on our page.

3. How to find GCD of 585, 414, 996 on a calculator?

You can find the GCD of 585, 414, 996 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.