GCD of 414, 224, 408 Calculator

Given Input numbers are 414, 224, 408

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 224

List of positive integer divisors of 224 that divides 224 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224

Divisors of 408

List of positive integer divisors of 408 that divides 408 without a remainder.

1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408

Greatest Common Divisior

We found the divisors of 414, 224, 408 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 414, 224, 408 is 2.

Therefore, GCD of numbers 414, 224, 408 is 2

Given Input Data is 414, 224, 408

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 224 is 2 x 2 x 2 x 2 x 2 x 7

Prime Factorization of 408 is 2 x 2 x 2 x 3 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, 224) = 46368

GCD(414, 224) = ( 414 x 224 ) / 46368

GCD(414, 224) = 92736 / 46368

GCD(414, 224) = 2

Step2:

Here we consider the GCD from the above i.e. 2 as first number and the next as 408

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

LCM(2, 408) = 408

GCD(2, 408) = ( 2 x 408 ) / 408

GCD(2, 408) = 816 / 408

GCD(2, 408) = 2

GCD of 414, 224, 408 is 2

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1. What is the GCD of 414, 224, 408?

GCD of 414, 224, 408 is 2

2. Where do I get the detailed procedure to find GCD of 414, 224, 408?

You can find a detailed procedure to find GCD of 414, 224, 408 on our page.

3. How to find GCD of 414, 224, 408 on a calculator?

You can find the GCD of 414, 224, 408 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.