Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Make use of GCD Calculator to determine the Greatest Common Divisor of 729, 282, 75, 108 i.e. 3 largest integer that divides all the numbers equally.
GCD of 729, 282, 75, 108 is 3
GCD(729, 282, 75, 108) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 729, 282, 75, 108 is 3
GCD(729, 282, 75, 108) = 3
Given Input numbers are 729, 282, 75, 108
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 729
List of positive integer divisors of 729 that divides 729 without a remainder.
1, 3, 9, 27, 81, 243, 729
Divisors of 282
List of positive integer divisors of 282 that divides 282 without a remainder.
1, 2, 3, 6, 47, 94, 141, 282
Divisors of 75
List of positive integer divisors of 75 that divides 75 without a remainder.
1, 3, 5, 15, 25, 75
Divisors of 108
List of positive integer divisors of 108 that divides 108 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Greatest Common Divisior
We found the divisors of 729, 282, 75, 108 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 729, 282, 75, 108 is 3.
Therefore, GCD of numbers 729, 282, 75, 108 is 3
Given Input Data is 729, 282, 75, 108
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 729 is 3 x 3 x 3 x 3 x 3 x 3
Prime Factorization of 282 is 2 x 3 x 47
Prime Factorization of 75 is 3 x 5 x 5
Prime Factorization of 108 is 2 x 2 x 3 x 3 x 3
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(729, 282) = 68526
GCD(729, 282) = ( 729 x 282 ) / 68526
GCD(729, 282) = 205578 / 68526
GCD(729, 282) = 3
Step2:
Here we consider the GCD from the above i.e. 3 as first number and the next as 75
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 75) = 75
GCD(3, 75) = ( 3 x 75 ) / 75
GCD(3, 75) = 225 / 75
GCD(3, 75) = 3
Step3:
Here we consider the GCD from the above i.e. 3 as first number and the next as 108
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 108) = 108
GCD(3, 108) = ( 3 x 108 ) / 108
GCD(3, 108) = 324 / 108
GCD(3, 108) = 3
GCD of 729, 282, 75, 108 is 3
Here are some samples of GCD of Numbers calculations.
1. What is the GCD of 729, 282, 75, 108?
GCD of 729, 282, 75, 108 is 3
2. Where do I get the detailed procedure to find GCD of 729, 282, 75, 108?
You can find a detailed procedure to find GCD of 729, 282, 75, 108 on our page.
3. How to find GCD of 729, 282, 75, 108 on a calculator?
You can find the GCD of 729, 282, 75, 108 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.