GCD of 21, 42, 39, 60 Calculator

Given Input numbers are 21, 42, 39, 60

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

Divisors of 21

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

1, 3, 7, 21

Divisors of 42

List of positive integer divisors of 42 that divides 42 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42

Divisors of 39

List of positive integer divisors of 39 that divides 39 without a remainder.

1, 3, 13, 39

Divisors of 60

List of positive integer divisors of 60 that divides 60 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Greatest Common Divisior

We found the divisors of 21, 42, 39, 60 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 21, 42, 39, 60 is 3.

Therefore, GCD of numbers 21, 42, 39, 60 is 3

Given Input Data is 21, 42, 39, 60

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

Prime Factorization of 21 is 3 x 7

Prime Factorization of 42 is 2 x 3 x 7

Prime Factorization of 39 is 3 x 13

Prime Factorization of 60 is 2 x 2 x 3 x 5

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(21, 42) = 42

GCD(21, 42) = ( 21 x 42 ) / 42

GCD(21, 42) = 882 / 42

GCD(21, 42) = 21

Step2:

Here we consider the GCD from the above i.e. 21 as first number and the next as 39

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

LCM(21, 39) = 273

GCD(21, 39) = ( 21 x 39 ) / 273

GCD(21, 39) = 819 / 273

GCD(21, 39) = 3

Step3:

Here we consider the GCD from the above i.e. 3 as first number and the next as 60

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

LCM(3, 60) = 60

GCD(3, 60) = ( 3 x 60 ) / 60

GCD(3, 60) = 180 / 60

GCD(3, 60) = 3

GCD of 21, 42, 39, 60 is 3

Here are some samples of GCD of Numbers calculations.

• GCD of 89, 75, 86, 96
• GCD of 23, 40, 84, 89
• GCD of 18, 12, 11, 94
• GCD of 84, 37, 67, 30
• GCD of 69, 99, 62, 69

1. What is the GCD of 21, 42, 39, 60?

GCD of 21, 42, 39, 60 is 3

2. Where do I get the detailed procedure to find GCD of 21, 42, 39, 60?

You can find a detailed procedure to find GCD of 21, 42, 39, 60 on our page.

3. How to find GCD of 21, 42, 39, 60 on a calculator?

You can find the GCD of 21, 42, 39, 60 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.