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 420, 654, 489, 516 i.e. 3 largest integer that divides all the numbers equally.
GCD of 420, 654, 489, 516 is 3
GCD(420, 654, 489, 516) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 420, 654, 489, 516 is 3
GCD(420, 654, 489, 516) = 3
Given Input numbers are 420, 654, 489, 516
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 420
List of positive integer divisors of 420 that divides 420 without a remainder.
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
Divisors of 654
List of positive integer divisors of 654 that divides 654 without a remainder.
1, 2, 3, 6, 109, 218, 327, 654
Divisors of 489
List of positive integer divisors of 489 that divides 489 without a remainder.
1, 3, 163, 489
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
Greatest Common Divisior
We found the divisors of 420, 654, 489, 516 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 420, 654, 489, 516 is 3.
Therefore, GCD of numbers 420, 654, 489, 516 is 3
Given Input Data is 420, 654, 489, 516
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 420 is 2 x 2 x 3 x 5 x 7
Prime Factorization of 654 is 2 x 3 x 109
Prime Factorization of 489 is 3 x 163
Prime Factorization of 516 is 2 x 2 x 3 x 43
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(420, 654) = 45780
GCD(420, 654) = ( 420 x 654 ) / 45780
GCD(420, 654) = 274680 / 45780
GCD(420, 654) = 6
Step2:
Here we consider the GCD from the above i.e. 6 as first number and the next as 489
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(6, 489) = 978
GCD(6, 489) = ( 6 x 489 ) / 978
GCD(6, 489) = 2934 / 978
GCD(6, 489) = 3
Step3:
Here we consider the GCD from the above i.e. 3 as first number and the next as 516
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 516) = 516
GCD(3, 516) = ( 3 x 516 ) / 516
GCD(3, 516) = 1548 / 516
GCD(3, 516) = 3
GCD of 420, 654, 489, 516 is 3
Here are some samples of GCD of Numbers calculations.
1. What is the GCD of 420, 654, 489, 516?
GCD of 420, 654, 489, 516 is 3
2. Where do I get the detailed procedure to find GCD of 420, 654, 489, 516?
You can find a detailed procedure to find GCD of 420, 654, 489, 516 on our page.
3. How to find GCD of 420, 654, 489, 516 on a calculator?
You can find the GCD of 420, 654, 489, 516 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.