GCD of 200, 480, 106, 644 Calculator

Given Input numbers are 200, 480, 106, 644

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

Divisors of 200

List of positive integer divisors of 200 that divides 200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

Divisors of 480

List of positive integer divisors of 480 that divides 480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480

Divisors of 106

List of positive integer divisors of 106 that divides 106 without a remainder.

1, 2, 53, 106

Divisors of 644

List of positive integer divisors of 644 that divides 644 without a remainder.

1, 2, 4, 7, 14, 23, 28, 46, 92, 161, 322, 644

Greatest Common Divisior

We found the divisors of 200, 480, 106, 644 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 200, 480, 106, 644 is 2.

Therefore, GCD of numbers 200, 480, 106, 644 is 2

Given Input Data is 200, 480, 106, 644

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

Prime Factorization of 200 is 2 x 2 x 2 x 5 x 5

Prime Factorization of 480 is 2 x 2 x 2 x 2 x 2 x 3 x 5

Prime Factorization of 106 is 2 x 53

Prime Factorization of 644 is 2 x 2 x 7 x 23

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(200, 480) = 2400

GCD(200, 480) = ( 200 x 480 ) / 2400

GCD(200, 480) = 96000 / 2400

GCD(200, 480) = 40

Step2:

Here we consider the GCD from the above i.e. 40 as first number and the next as 106

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

LCM(40, 106) = 2120

GCD(40, 106) = ( 40 x 106 ) / 2120

GCD(40, 106) = 4240 / 2120

GCD(40, 106) = 2

Step3:

Here we consider the GCD from the above i.e. 2 as first number and the next as 644

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

LCM(2, 644) = 644

GCD(2, 644) = ( 2 x 644 ) / 644

GCD(2, 644) = 1288 / 644

GCD(2, 644) = 2

GCD of 200, 480, 106, 644 is 2

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1. What is the GCD of 200, 480, 106, 644?

GCD of 200, 480, 106, 644 is 2

2. Where do I get the detailed procedure to find GCD of 200, 480, 106, 644?

You can find a detailed procedure to find GCD of 200, 480, 106, 644 on our page.

3. How to find GCD of 200, 480, 106, 644 on a calculator?

You can find the GCD of 200, 480, 106, 644 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.