GCD of 675, 684, 723 Calculator

Given Input numbers are 675, 684, 723

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

Divisors of 675

List of positive integer divisors of 675 that divides 675 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675

Divisors of 684

List of positive integer divisors of 684 that divides 684 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684

Divisors of 723

List of positive integer divisors of 723 that divides 723 without a remainder.

1, 3, 241, 723

Greatest Common Divisior

We found the divisors of 675, 684, 723 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 675, 684, 723 is 3.

Therefore, GCD of numbers 675, 684, 723 is 3

Given Input Data is 675, 684, 723

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

Prime Factorization of 675 is 3 x 3 x 3 x 5 x 5

Prime Factorization of 684 is 2 x 2 x 3 x 3 x 19

Prime Factorization of 723 is 3 x 241

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(675, 684) = 51300

GCD(675, 684) = ( 675 x 684 ) / 51300

GCD(675, 684) = 461700 / 51300

GCD(675, 684) = 9

Step2:

Here we consider the GCD from the above i.e. 9 as first number and the next as 723

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

LCM(9, 723) = 2169

GCD(9, 723) = ( 9 x 723 ) / 2169

GCD(9, 723) = 6507 / 2169

GCD(9, 723) = 3

GCD of 675, 684, 723 is 3

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1. What is the GCD of 675, 684, 723?

GCD of 675, 684, 723 is 3

2. Where do I get the detailed procedure to find GCD of 675, 684, 723?

You can find a detailed procedure to find GCD of 675, 684, 723 on our page.

3. How to find GCD of 675, 684, 723 on a calculator?

You can find the GCD of 675, 684, 723 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.