GCD of 54, 300, 620, 414 Calculator

Given Input numbers are 54, 300, 620, 414

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

Divisors of 54

List of positive integer divisors of 54 that divides 54 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54

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 620

List of positive integer divisors of 620 that divides 620 without a remainder.

1, 2, 4, 5, 10, 20, 31, 62, 124, 155, 310, 620

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

Greatest Common Divisior

We found the divisors of 54, 300, 620, 414 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 54, 300, 620, 414 is 2.

Therefore, GCD of numbers 54, 300, 620, 414 is 2

Given Input Data is 54, 300, 620, 414

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

Prime Factorization of 54 is 2 x 3 x 3 x 3

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

Prime Factorization of 620 is 2 x 2 x 5 x 31

Prime Factorization of 414 is 2 x 3 x 3 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(54, 300) = 2700

GCD(54, 300) = ( 54 x 300 ) / 2700

GCD(54, 300) = 16200 / 2700

GCD(54, 300) = 6

Step2:

Here we consider the GCD from the above i.e. 6 as first number and the next as 620

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

LCM(6, 620) = 1860

GCD(6, 620) = ( 6 x 620 ) / 1860

GCD(6, 620) = 3720 / 1860

GCD(6, 620) = 2

Step3:

Here we consider the GCD from the above i.e. 2 as first number and the next as 414

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

LCM(2, 414) = 414

GCD(2, 414) = ( 2 x 414 ) / 414

GCD(2, 414) = 828 / 414

GCD(2, 414) = 2

GCD of 54, 300, 620, 414 is 2

Here are some samples of GCD of Numbers calculations.

• GCD of 50, 528, 242, 540
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• GCD of 56, 986, 608, 720
• GCD of 98, 393, 851, 742
• GCD of 56, 789, 112, 420

1. What is the GCD of 54, 300, 620, 414?

GCD of 54, 300, 620, 414 is 2

2. Where do I get the detailed procedure to find GCD of 54, 300, 620, 414?

You can find a detailed procedure to find GCD of 54, 300, 620, 414 on our page.

3. How to find GCD of 54, 300, 620, 414 on a calculator?

You can find the GCD of 54, 300, 620, 414 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.