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 516, 135, 69, 975 i.e. 3 largest integer that divides all the numbers equally.
GCD of 516, 135, 69, 975 is 3
GCD(516, 135, 69, 975) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 516, 135, 69, 975 is 3
GCD(516, 135, 69, 975) = 3
Given Input numbers are 516, 135, 69, 975
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 516
List of positive integer divisors of 516 that divides 516 without a remainder.
1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
Divisors of 135
List of positive integer divisors of 135 that divides 135 without a remainder.
1, 3, 5, 9, 15, 27, 45, 135
Divisors of 69
List of positive integer divisors of 69 that divides 69 without a remainder.
1, 3, 23, 69
Divisors of 975
List of positive integer divisors of 975 that divides 975 without a remainder.
1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
Greatest Common Divisior
We found the divisors of 516, 135, 69, 975 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 516, 135, 69, 975 is 3.
Therefore, GCD of numbers 516, 135, 69, 975 is 3
Given Input Data is 516, 135, 69, 975
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 516 is 2 x 2 x 3 x 43
Prime Factorization of 135 is 3 x 3 x 3 x 5
Prime Factorization of 69 is 3 x 23
Prime Factorization of 975 is 3 x 5 x 5 x 13
Highest common occurrences in the given inputs are 31
Multiplying them we get the GCD as 3
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(516, 135) = 23220
GCD(516, 135) = ( 516 x 135 ) / 23220
GCD(516, 135) = 69660 / 23220
GCD(516, 135) = 3
Step2:
Here we consider the GCD from the above i.e. 3 as first number and the next as 69
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 69) = 69
GCD(3, 69) = ( 3 x 69 ) / 69
GCD(3, 69) = 207 / 69
GCD(3, 69) = 3
Step3:
Here we consider the GCD from the above i.e. 3 as first number and the next as 975
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 975) = 975
GCD(3, 975) = ( 3 x 975 ) / 975
GCD(3, 975) = 2925 / 975
GCD(3, 975) = 3
GCD of 516, 135, 69, 975 is 3
Here are some samples of GCD of Numbers calculations.
1. What is the GCD of 516, 135, 69, 975?
GCD of 516, 135, 69, 975 is 3
2. Where do I get the detailed procedure to find GCD of 516, 135, 69, 975?
You can find a detailed procedure to find GCD of 516, 135, 69, 975 on our page.
3. How to find GCD of 516, 135, 69, 975 on a calculator?
You can find the GCD of 516, 135, 69, 975 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.