Make use of GCD Calculator to determine the Greatest Common Divisor of 214, 400, 306, 640 i.e. 2 largest integer that divides all the numbers equally.

GCD of 214, 400, 306, 640 is 2

GCD(214, 400, 306, 640) = 2

**Ex:** 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345

GCD of numbers 214, 400, 306, 640 is 2

GCD(214, 400, 306, 640) = 2

Given Input numbers are 214, 400, 306, 640

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

**Divisors of 214**

List of positive integer divisors of 214 that divides 214 without a remainder.

1, 2, 107, 214

**Divisors of 400**

List of positive integer divisors of 400 that divides 400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

**Divisors of 306**

List of positive integer divisors of 306 that divides 306 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306

**Divisors of 640**

List of positive integer divisors of 640 that divides 640 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 320, 640

**Greatest Common Divisior**

We found the divisors of 214, 400, 306, 640 . The biggest common divisior number is the **GCD** number.

So the **Greatest Common Divisior 214, 400, 306, 640 ** is **2**.

Therefore, GCD of numbers 214, 400, 306, 640 is 2

Given Input Data is 214, 400, 306, 640

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

Prime Factorization of 214 is 2 x 107

Prime Factorization of 400 is 2 x 2 x 2 x 2 x 5 x 5

Prime Factorization of 306 is 2 x 3 x 3 x 17

Prime Factorization of 640 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5

Highest common occurrences in the given inputs are 2^{1}

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(214, 400) = 42800

GCD(214, 400) = ( 214 x 400 ) / 42800

GCD(214, 400) = 85600 / 42800

GCD(214, 400) = 2

**Step2:**

Here we consider the GCD from the above i.e. 2 as first number and the next as 306

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

LCM(2, 306) = 306

GCD(2, 306) = ( 2 x 306 ) / 306

GCD(2, 306) = 612 / 306

GCD(2, 306) = 2

**Step3:**

Here we consider the GCD from the above i.e. 2 as first number and the next as 640

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

LCM(2, 640) = 640

GCD(2, 640) = ( 2 x 640 ) / 640

GCD(2, 640) = 1280 / 640

GCD(2, 640) = 2

GCD of 214, 400, 306, 640 is 2

Here are some samples of GCD of Numbers calculations.

**1. What is the GCD of 214, 400, 306, 640?**

GCD of 214, 400, 306, 640 is 2

**2. Where do I get the detailed procedure to find GCD of 214, 400, 306, 640?**

You can find a detailed procedure to find GCD of 214, 400, 306, 640 on our page.

**3. How to find GCD of 214, 400, 306, 640 on a calculator?**

You can find the GCD of 214, 400, 306, 640 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.