GCD of 209, 300, 85, 105 Calculator

Given Input numbers are 209, 300, 85, 105

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

Divisors of 209

List of positive integer divisors of 209 that divides 209 without a remainder.

1, 11, 19, 209

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 85

List of positive integer divisors of 85 that divides 85 without a remainder.

1, 5, 17, 85

Divisors of 105

List of positive integer divisors of 105 that divides 105 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105

Greatest Common Divisior

We found the divisors of 209, 300, 85, 105 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 209, 300, 85, 105 is 1.

Therefore, GCD of numbers 209, 300, 85, 105 is 1

Given Input Data is 209, 300, 85, 105

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

Prime Factorization of 209 is 11 x 19

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

Prime Factorization of 85 is 5 x 17

Prime Factorization of 105 is 3 x 5 x 7

The above numbers do not have any common prime factor. So GCD is 1

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(209, 300) = 62700

GCD(209, 300) = ( 209 x 300 ) / 62700

GCD(209, 300) = 62700 / 62700

GCD(209, 300) = 1

Step2:

Here we consider the GCD from the above i.e. 1 as first number and the next as 85

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

LCM(1, 85) = 85

GCD(1, 85) = ( 1 x 85 ) / 85

GCD(1, 85) = 85 / 85

GCD(1, 85) = 1

Step3:

Here we consider the GCD from the above i.e. 1 as first number and the next as 105

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

LCM(1, 105) = 105

GCD(1, 105) = ( 1 x 105 ) / 105

GCD(1, 105) = 105 / 105

GCD(1, 105) = 1

GCD of 209, 300, 85, 105 is 1

Here are some samples of GCD of Numbers calculations.

• GCD of 999, 393, 17, 264
• GCD of 627, 566, 85, 421
• GCD of 883, 875, 67, 449
• GCD of 603, 892, 99, 760
• GCD of 566, 702, 33, 355

1. What is the GCD of 209, 300, 85, 105?

GCD of 209, 300, 85, 105 is 1

2. Where do I get the detailed procedure to find GCD of 209, 300, 85, 105?

You can find a detailed procedure to find GCD of 209, 300, 85, 105 on our page.

3. How to find GCD of 209, 300, 85, 105 on a calculator?

You can find the GCD of 209, 300, 85, 105 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.