GCD of 414, 216, 716, 578 Calculator

Given Input numbers are 414, 216, 716, 578

To find the GCD of numbers using factoring list out all the divisors of each number

Divisors of 414

List of positive integer divisors of 414 that divides 414 without a remainder.

1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414

Divisors of 216

List of positive integer divisors of 216 that divides 216 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

Divisors of 716

List of positive integer divisors of 716 that divides 716 without a remainder.

1, 2, 4, 179, 358, 716

Divisors of 578

List of positive integer divisors of 578 that divides 578 without a remainder.

1, 2, 17, 34, 289, 578

Greatest Common Divisior

We found the divisors of 414, 216, 716, 578 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 414, 216, 716, 578 is 2.

Therefore, GCD of numbers 414, 216, 716, 578 is 2

Given Input Data is 414, 216, 716, 578

Make a list of Prime Factors of all the given numbers initially

Prime Factorization of 414 is 2 x 3 x 3 x 23

Prime Factorization of 216 is 2 x 2 x 2 x 3 x 3 x 3

Prime Factorization of 716 is 2 x 2 x 179

Prime Factorization of 578 is 2 x 17 x 17

Highest common occurrences in the given inputs are 2¹

Multiplying them we get the GCD as 2

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(414, 216) = 4968

GCD(414, 216) = ( 414 x 216 ) / 4968

GCD(414, 216) = 89424 / 4968

GCD(414, 216) = 18

Step2:

Here we consider the GCD from the above i.e. 18 as first number and the next as 716

The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)

LCM(18, 716) = 6444

GCD(18, 716) = ( 18 x 716 ) / 6444

GCD(18, 716) = 12888 / 6444

GCD(18, 716) = 2

Step3:

Here we consider the GCD from the above i.e. 2 as first number and the next as 578

The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)

LCM(2, 578) = 578

GCD(2, 578) = ( 2 x 578 ) / 578

GCD(2, 578) = 1156 / 578

GCD(2, 578) = 2

GCD of 414, 216, 716, 578 is 2

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1. What is the GCD of 414, 216, 716, 578?

GCD of 414, 216, 716, 578 is 2

2. Where do I get the detailed procedure to find GCD of 414, 216, 716, 578?

You can find a detailed procedure to find GCD of 414, 216, 716, 578 on our page.

3. How to find GCD of 414, 216, 716, 578 on a calculator?

You can find the GCD of 414, 216, 716, 578 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.