GCD of 54, 84, 21 Calculator
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 54, 84, 21 i.e. 3 largest integer that divides all the numbers equally.
GCD of 54, 84, 21 is 3
GCD(54, 84, 21) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 54, 84, 21 is 3
GCD(54, 84, 21) = 3
GCDof 54,84,21 is 3
Given Input numbers are 54, 84, 21
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 54
List of positive integer divisors of 54 that divides 54 without a remainder.
1, 2, 3, 6, 9, 18, 27, 54
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
Divisors of 21
List of positive integer divisors of 21 that divides 21 without a remainder.
1, 3, 7, 21
Greatest Common Divisior
We found the divisors of 54, 84, 21 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 54, 84, 21 is 3.
Therefore, GCD of numbers 54, 84, 21 is 3
Given Input Data is 54, 84, 21
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 54 is 2 x 3 x 3 x 3
Prime Factorization of 84 is 2 x 2 x 3 x 7
Prime Factorization of 21 is 3 x 7
Highest common occurrences in the given inputs are 31
Multiplying them we get the GCD as 3
Finding GCD of 54, 84, 21 using LCM Formula
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(54, 84) = 756
GCD(54, 84) = ( 54 x 84 ) / 756
GCD(54, 84) = 4536 / 756
GCD(54, 84) = 6
Step2:
Here we consider the GCD from the above i.e. 6 as first number and the next as 21
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(6, 21) = 42
GCD(6, 21) = ( 6 x 21 ) / 42
GCD(6, 21) = 126 / 42
GCD(6, 21) = 3
GCD of 54, 84, 21 is 3
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FAQs on GCD of numbers 54, 84, 21
1. What is the GCD of 54, 84, 21?
GCD of 54, 84, 21 is 3
2. Where do I get the detailed procedure to find GCD of 54, 84, 21?
You can find a detailed procedure to find GCD of 54, 84, 21 on our page.
3. How to find GCD of 54, 84, 21 on a calculator?
You can find the GCD of 54, 84, 21 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.