GCD of 45, 36, 99, 21 Calculator

Given Input numbers are 45, 36, 99, 21

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

Divisors of 45

List of positive integer divisors of 45 that divides 45 without a remainder.

1, 3, 5, 9, 15, 45

Divisors of 36

List of positive integer divisors of 36 that divides 36 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36

Divisors of 99

List of positive integer divisors of 99 that divides 99 without a remainder.

1, 3, 9, 11, 33, 99

Divisors of 21

List of positive integer divisors of 21 that divides 21 without a remainder.

1, 3, 7, 21

Greatest Common Divisior

We found the divisors of 45, 36, 99, 21 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 45, 36, 99, 21 is 3.

Therefore, GCD of numbers 45, 36, 99, 21 is 3

Given Input Data is 45, 36, 99, 21

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

Prime Factorization of 45 is 3 x 3 x 5

Prime Factorization of 36 is 2 x 2 x 3 x 3

Prime Factorization of 99 is 3 x 3 x 11

Prime Factorization of 21 is 3 x 7

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(45, 36) = 180

GCD(45, 36) = ( 45 x 36 ) / 180

GCD(45, 36) = 1620 / 180

GCD(45, 36) = 9

Step2:

Here we consider the GCD from the above i.e. 9 as first number and the next as 99

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

LCM(9, 99) = 99

GCD(9, 99) = ( 9 x 99 ) / 99

GCD(9, 99) = 891 / 99

GCD(9, 99) = 9

Step3:

Here we consider the GCD from the above i.e. 9 as first number and the next as 21

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

LCM(9, 21) = 63

GCD(9, 21) = ( 9 x 21 ) / 63

GCD(9, 21) = 189 / 63

GCD(9, 21) = 3

GCD of 45, 36, 99, 21 is 3

Here are some samples of GCD of Numbers calculations.

• GCD of 12, 61, 13, 80
• GCD of 41, 46, 33, 77
• GCD of 67, 88, 88, 92
• GCD of 73, 97, 73, 10
• GCD of 23, 88, 98, 73

1. What is the GCD of 45, 36, 99, 21?

GCD of 45, 36, 99, 21 is 3

2. Where do I get the detailed procedure to find GCD of 45, 36, 99, 21?

You can find a detailed procedure to find GCD of 45, 36, 99, 21 on our page.

3. How to find GCD of 45, 36, 99, 21 on a calculator?

You can find the GCD of 45, 36, 99, 21 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.