GCD of 12, 66, 69 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 12, 66, 69 i.e. 3 largest integer that divides all the numbers equally.
GCD of 12, 66, 69 is 3
GCD(12, 66, 69) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 12, 66, 69 is 3
GCD(12, 66, 69) = 3
GCDof 12,66,69 is 3
Given Input numbers are 12, 66, 69
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 12
List of positive integer divisors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Divisors of 66
List of positive integer divisors of 66 that divides 66 without a remainder.
1, 2, 3, 6, 11, 22, 33, 66
Divisors of 69
List of positive integer divisors of 69 that divides 69 without a remainder.
1, 3, 23, 69
Greatest Common Divisior
We found the divisors of 12, 66, 69 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 12, 66, 69 is 3.
Therefore, GCD of numbers 12, 66, 69 is 3
Given Input Data is 12, 66, 69
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 12 is 2 x 2 x 3
Prime Factorization of 66 is 2 x 3 x 11
Prime Factorization of 69 is 3 x 23
Highest common occurrences in the given inputs are 31
Multiplying them we get the GCD as 3
Finding GCD of 12, 66, 69 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(12, 66) = 132
GCD(12, 66) = ( 12 x 66 ) / 132
GCD(12, 66) = 792 / 132
GCD(12, 66) = 6
Step2:
Here we consider the GCD from the above i.e. 6 as first number and the next as 69
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(6, 69) = 138
GCD(6, 69) = ( 6 x 69 ) / 138
GCD(6, 69) = 414 / 138
GCD(6, 69) = 3
GCD of 12, 66, 69 is 3
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FAQs on GCD of numbers 12, 66, 69
1. What is the GCD of 12, 66, 69?
GCD of 12, 66, 69 is 3
2. Where do I get the detailed procedure to find GCD of 12, 66, 69?
You can find a detailed procedure to find GCD of 12, 66, 69 on our page.
3. How to find GCD of 12, 66, 69 on a calculator?
You can find the GCD of 12, 66, 69 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.