GCD of 420, 654, 489, 516 Calculator

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

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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.