GCD of 78, 45, 84 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 78, 45, 84 i.e. 3 largest integer that divides all the numbers equally.
GCD of 78, 45, 84 is 3
GCD(78, 45, 84) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 78, 45, 84 is 3
GCD(78, 45, 84) = 3
GCDof 78,45,84 is 3
Given Input numbers are 78, 45, 84
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 78
List of positive integer divisors of 78 that divides 78 without a remainder.
1, 2, 3, 6, 13, 26, 39, 78
Divisors of 45
List of positive integer divisors of 45 that divides 45 without a remainder.
1, 3, 5, 9, 15, 45
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
Greatest Common Divisior
We found the divisors of 78, 45, 84 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 78, 45, 84 is 3.
Therefore, GCD of numbers 78, 45, 84 is 3
Given Input Data is 78, 45, 84
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 78 is 2 x 3 x 13
Prime Factorization of 45 is 3 x 3 x 5
Prime Factorization of 84 is 2 x 2 x 3 x 7
Highest common occurrences in the given inputs are 31
Multiplying them we get the GCD as 3
Finding GCD of 78, 45, 84 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(78, 45) = 1170
GCD(78, 45) = ( 78 x 45 ) / 1170
GCD(78, 45) = 3510 / 1170
GCD(78, 45) = 3
Step2:
Here we consider the GCD from the above i.e. 3 as first number and the next as 84
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 84) = 84
GCD(3, 84) = ( 3 x 84 ) / 84
GCD(3, 84) = 252 / 84
GCD(3, 84) = 3
GCD of 78, 45, 84 is 3
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FAQs on GCD of numbers 78, 45, 84
1. What is the GCD of 78, 45, 84?
GCD of 78, 45, 84 is 3
2. Where do I get the detailed procedure to find GCD of 78, 45, 84?
You can find a detailed procedure to find GCD of 78, 45, 84 on our page.
3. How to find GCD of 78, 45, 84 on a calculator?
You can find the GCD of 78, 45, 84 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.