GCD of 414, 172, 10, 686 Calculator

Given Input numbers are 414, 172, 10, 686

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 172

List of positive integer divisors of 172 that divides 172 without a remainder.

1, 2, 4, 43, 86, 172

Divisors of 10

List of positive integer divisors of 10 that divides 10 without a remainder.

1, 2, 5, 10

Divisors of 686

List of positive integer divisors of 686 that divides 686 without a remainder.

1, 2, 7, 14, 49, 98, 343, 686

Greatest Common Divisior

We found the divisors of 414, 172, 10, 686 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 414, 172, 10, 686 is 2.

Therefore, GCD of numbers 414, 172, 10, 686 is 2

Given Input Data is 414, 172, 10, 686

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 172 is 2 x 2 x 43

Prime Factorization of 10 is 2 x 5

Prime Factorization of 686 is 2 x 7 x 7 x 7

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, 172) = 35604

GCD(414, 172) = ( 414 x 172 ) / 35604

GCD(414, 172) = 71208 / 35604

GCD(414, 172) = 2

Step2:

Here we consider the GCD from the above i.e. 2 as first number and the next as 10

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

LCM(2, 10) = 10

GCD(2, 10) = ( 2 x 10 ) / 10

GCD(2, 10) = 20 / 10

GCD(2, 10) = 2

Step3:

Here we consider the GCD from the above i.e. 2 as first number and the next as 686

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

LCM(2, 686) = 686

GCD(2, 686) = ( 2 x 686 ) / 686

GCD(2, 686) = 1372 / 686

GCD(2, 686) = 2

GCD of 414, 172, 10, 686 is 2

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• GCD of 958, 958, 74, 349
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1. What is the GCD of 414, 172, 10, 686?

GCD of 414, 172, 10, 686 is 2

2. Where do I get the detailed procedure to find GCD of 414, 172, 10, 686?

You can find a detailed procedure to find GCD of 414, 172, 10, 686 on our page.

3. How to find GCD of 414, 172, 10, 686 on a calculator?

You can find the GCD of 414, 172, 10, 686 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.