GCD of 45, 12, 90 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 45, 12, 90 i.e. 3 largest integer that divides all the numbers equally.
GCD of 45, 12, 90 is 3
GCD(45, 12, 90) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 45, 12, 90 is 3
GCD(45, 12, 90) = 3
GCDof 45,12,90 is 3
Given Input numbers are 45, 12, 90
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 45
List of positive integer divisors of 45 that divides 45 without a remainder.
1, 3, 5, 9, 15, 45
Divisors of 12
List of positive integer divisors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Divisors of 90
List of positive integer divisors of 90 that divides 90 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Greatest Common Divisior
We found the divisors of 45, 12, 90 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 45, 12, 90 is 3.
Therefore, GCD of numbers 45, 12, 90 is 3
Given Input Data is 45, 12, 90
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 45 is 3 x 3 x 5
Prime Factorization of 12 is 2 x 2 x 3
Prime Factorization of 90 is 2 x 3 x 3 x 5
Highest common occurrences in the given inputs are 31
Multiplying them we get the GCD as 3
Finding GCD of 45, 12, 90 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(45, 12) = 180
GCD(45, 12) = ( 45 x 12 ) / 180
GCD(45, 12) = 540 / 180
GCD(45, 12) = 3
Step2:
Here we consider the GCD from the above i.e. 3 as first number and the next as 90
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 90) = 90
GCD(3, 90) = ( 3 x 90 ) / 90
GCD(3, 90) = 270 / 90
GCD(3, 90) = 3
GCD of 45, 12, 90 is 3
GCD of Numbers Calculation Examples
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FAQs on GCD of numbers 45, 12, 90
1. What is the GCD of 45, 12, 90?
GCD of 45, 12, 90 is 3
2. Where do I get the detailed procedure to find GCD of 45, 12, 90?
You can find a detailed procedure to find GCD of 45, 12, 90 on our page.
3. How to find GCD of 45, 12, 90 on a calculator?
You can find the GCD of 45, 12, 90 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.