GCD of 72, 54, 78 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 72, 54, 78 i.e. 6 largest integer that divides all the numbers equally.
GCD of 72, 54, 78 is 6
GCD(72, 54, 78) = 6
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 72, 54, 78 is 6
GCD(72, 54, 78) = 6
GCDof 72,54,78 is 6
Given Input numbers are 72, 54, 78
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 72
List of positive integer divisors of 72 that divides 72 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
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 78
List of positive integer divisors of 78 that divides 78 without a remainder.
1, 2, 3, 6, 13, 26, 39, 78
Greatest Common Divisior
We found the divisors of 72, 54, 78 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 72, 54, 78 is 6.
Therefore, GCD of numbers 72, 54, 78 is 6
Given Input Data is 72, 54, 78
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 72 is 2 x 2 x 2 x 3 x 3
Prime Factorization of 54 is 2 x 3 x 3 x 3
Prime Factorization of 78 is 2 x 3 x 13
Highest common occurrences in the given inputs are 21 x 31
Multiplying them we get the GCD as 6
Finding GCD of 72, 54, 78 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(72, 54) = 216
GCD(72, 54) = ( 72 x 54 ) / 216
GCD(72, 54) = 3888 / 216
GCD(72, 54) = 18
Step2:
Here we consider the GCD from the above i.e. 18 as first number and the next as 78
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(18, 78) = 234
GCD(18, 78) = ( 18 x 78 ) / 234
GCD(18, 78) = 1404 / 234
GCD(18, 78) = 6
GCD of 72, 54, 78 is 6
GCD of Numbers Calculation Examples
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FAQs on GCD of numbers 72, 54, 78
1. What is the GCD of 72, 54, 78?
GCD of 72, 54, 78 is 6
2. Where do I get the detailed procedure to find GCD of 72, 54, 78?
You can find a detailed procedure to find GCD of 72, 54, 78 on our page.
3. How to find GCD of 72, 54, 78 on a calculator?
You can find the GCD of 72, 54, 78 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.