GCD of 724, 408, 138, 412 Calculator

Given Input numbers are 724, 408, 138, 412

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

Divisors of 724

List of positive integer divisors of 724 that divides 724 without a remainder.

1, 2, 4, 181, 362, 724

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

Divisors of 138

List of positive integer divisors of 138 that divides 138 without a remainder.

1, 2, 3, 6, 23, 46, 69, 138

Divisors of 412

List of positive integer divisors of 412 that divides 412 without a remainder.

1, 2, 4, 103, 206, 412

Greatest Common Divisior

We found the divisors of 724, 408, 138, 412 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 724, 408, 138, 412 is 2.

Therefore, GCD of numbers 724, 408, 138, 412 is 2

Given Input Data is 724, 408, 138, 412

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

Prime Factorization of 724 is 2 x 2 x 181

Prime Factorization of 408 is 2 x 2 x 2 x 3 x 17

Prime Factorization of 138 is 2 x 3 x 23

Prime Factorization of 412 is 2 x 2 x 103

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(724, 408) = 73848

GCD(724, 408) = ( 724 x 408 ) / 73848

GCD(724, 408) = 295392 / 73848

GCD(724, 408) = 4

Step2:

Here we consider the GCD from the above i.e. 4 as first number and the next as 138

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

LCM(4, 138) = 276

GCD(4, 138) = ( 4 x 138 ) / 276

GCD(4, 138) = 552 / 276

GCD(4, 138) = 2

Step3:

Here we consider the GCD from the above i.e. 2 as first number and the next as 412

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

LCM(2, 412) = 412

GCD(2, 412) = ( 2 x 412 ) / 412

GCD(2, 412) = 824 / 412

GCD(2, 412) = 2

GCD of 724, 408, 138, 412 is 2

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1. What is the GCD of 724, 408, 138, 412?

GCD of 724, 408, 138, 412 is 2

2. Where do I get the detailed procedure to find GCD of 724, 408, 138, 412?

You can find a detailed procedure to find GCD of 724, 408, 138, 412 on our page.

3. How to find GCD of 724, 408, 138, 412 on a calculator?

You can find the GCD of 724, 408, 138, 412 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.