GCD of 172, 414, 16, 854 Calculator

Given Input numbers are 172, 414, 16, 854

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

Divisors of 172

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

1, 2, 4, 43, 86, 172

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 16

List of positive integer divisors of 16 that divides 16 without a remainder.

1, 2, 4, 8, 16

Divisors of 854

List of positive integer divisors of 854 that divides 854 without a remainder.

1, 2, 7, 14, 61, 122, 427, 854

Greatest Common Divisior

We found the divisors of 172, 414, 16, 854 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 172, 414, 16, 854 is 2.

Therefore, GCD of numbers 172, 414, 16, 854 is 2

Given Input Data is 172, 414, 16, 854

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

Prime Factorization of 172 is 2 x 2 x 43

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

Prime Factorization of 16 is 2 x 2 x 2 x 2

Prime Factorization of 854 is 2 x 7 x 61

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(172, 414) = 35604

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

GCD(172, 414) = 71208 / 35604

GCD(172, 414) = 2

Step2:

Here we consider the GCD from the above i.e. 2 as first number and the next as 16

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

LCM(2, 16) = 16

GCD(2, 16) = ( 2 x 16 ) / 16

GCD(2, 16) = 32 / 16

GCD(2, 16) = 2

Step3:

Here we consider the GCD from the above i.e. 2 as first number and the next as 854

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

LCM(2, 854) = 854

GCD(2, 854) = ( 2 x 854 ) / 854

GCD(2, 854) = 1708 / 854

GCD(2, 854) = 2

GCD of 172, 414, 16, 854 is 2

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1. What is the GCD of 172, 414, 16, 854?

GCD of 172, 414, 16, 854 is 2

2. Where do I get the detailed procedure to find GCD of 172, 414, 16, 854?

You can find a detailed procedure to find GCD of 172, 414, 16, 854 on our page.

3. How to find GCD of 172, 414, 16, 854 on a calculator?

You can find the GCD of 172, 414, 16, 854 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.