GCD of 90, 600, 309, 345 Calculator

Given Input numbers are 90, 600, 309, 345

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

Divisors of 90

List of positive integer divisors of 90 that divides 90 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Divisors of 600

List of positive integer divisors of 600 that divides 600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600

Divisors of 309

List of positive integer divisors of 309 that divides 309 without a remainder.

1, 3, 103, 309

Divisors of 345

List of positive integer divisors of 345 that divides 345 without a remainder.

1, 3, 5, 15, 23, 69, 115, 345

Greatest Common Divisior

We found the divisors of 90, 600, 309, 345 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 90, 600, 309, 345 is 3.

Therefore, GCD of numbers 90, 600, 309, 345 is 3

Given Input Data is 90, 600, 309, 345

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

Prime Factorization of 90 is 2 x 3 x 3 x 5

Prime Factorization of 600 is 2 x 2 x 2 x 3 x 5 x 5

Prime Factorization of 309 is 3 x 103

Prime Factorization of 345 is 3 x 5 x 23

Highest common occurrences in the given inputs are 3¹

Multiplying them we get the GCD as 3

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(90, 600) = 1800

GCD(90, 600) = ( 90 x 600 ) / 1800

GCD(90, 600) = 54000 / 1800

GCD(90, 600) = 30

Step2:

Here we consider the GCD from the above i.e. 30 as first number and the next as 309

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

LCM(30, 309) = 3090

GCD(30, 309) = ( 30 x 309 ) / 3090

GCD(30, 309) = 9270 / 3090

GCD(30, 309) = 3

Step3:

Here we consider the GCD from the above i.e. 3 as first number and the next as 345

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

LCM(3, 345) = 345

GCD(3, 345) = ( 3 x 345 ) / 345

GCD(3, 345) = 1035 / 345

GCD(3, 345) = 3

GCD of 90, 600, 309, 345 is 3

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• GCD of 10, 811, 593, 870
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1. What is the GCD of 90, 600, 309, 345?

GCD of 90, 600, 309, 345 is 3

2. Where do I get the detailed procedure to find GCD of 90, 600, 309, 345?

You can find a detailed procedure to find GCD of 90, 600, 309, 345 on our page.

3. How to find GCD of 90, 600, 309, 345 on a calculator?

You can find the GCD of 90, 600, 309, 345 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.