GCD of 138, 300, 820 Calculator

Given Input numbers are 138, 300, 820

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

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 300

List of positive integer divisors of 300 that divides 300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

Divisors of 820

List of positive integer divisors of 820 that divides 820 without a remainder.

1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820

Greatest Common Divisior

We found the divisors of 138, 300, 820 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 138, 300, 820 is 2.

Therefore, GCD of numbers 138, 300, 820 is 2

Given Input Data is 138, 300, 820

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

Prime Factorization of 138 is 2 x 3 x 23

Prime Factorization of 300 is 2 x 2 x 3 x 5 x 5

Prime Factorization of 820 is 2 x 2 x 5 x 41

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(138, 300) = 6900

GCD(138, 300) = ( 138 x 300 ) / 6900

GCD(138, 300) = 41400 / 6900

GCD(138, 300) = 6

Step2:

Here we consider the GCD from the above i.e. 6 as first number and the next as 820

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

LCM(6, 820) = 2460

GCD(6, 820) = ( 6 x 820 ) / 2460

GCD(6, 820) = 4920 / 2460

GCD(6, 820) = 2

GCD of 138, 300, 820 is 2

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1. What is the GCD of 138, 300, 820?

GCD of 138, 300, 820 is 2

2. Where do I get the detailed procedure to find GCD of 138, 300, 820?

You can find a detailed procedure to find GCD of 138, 300, 820 on our page.

3. How to find GCD of 138, 300, 820 on a calculator?

You can find the GCD of 138, 300, 820 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.