GCD of 84, 54, 18, 14 Calculator

Given Input numbers are 84, 54, 18, 14

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

Divisors of 84

List of positive integer divisors of 84 that divides 84 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

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 18

List of positive integer divisors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

Divisors of 14

List of positive integer divisors of 14 that divides 14 without a remainder.

1, 2, 7, 14

Greatest Common Divisior

We found the divisors of 84, 54, 18, 14 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 84, 54, 18, 14 is 2.

Therefore, GCD of numbers 84, 54, 18, 14 is 2

Given Input Data is 84, 54, 18, 14

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

Prime Factorization of 84 is 2 x 2 x 3 x 7

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

Prime Factorization of 18 is 2 x 3 x 3

Prime Factorization of 14 is 2 x 7

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(84, 54) = 756

GCD(84, 54) = ( 84 x 54 ) / 756

GCD(84, 54) = 4536 / 756

GCD(84, 54) = 6

Step2:

Here we consider the GCD from the above i.e. 6 as first number and the next as 18

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

LCM(6, 18) = 18

GCD(6, 18) = ( 6 x 18 ) / 18

GCD(6, 18) = 108 / 18

GCD(6, 18) = 6

Step3:

Here we consider the GCD from the above i.e. 6 as first number and the next as 14

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

LCM(6, 14) = 42

GCD(6, 14) = ( 6 x 14 ) / 42

GCD(6, 14) = 84 / 42

GCD(6, 14) = 2

GCD of 84, 54, 18, 14 is 2

Here are some samples of GCD of Numbers calculations.

• GCD of 81, 24, 28, 24
• GCD of 79, 43, 89, 57
• GCD of 18, 81, 11, 98
• GCD of 60, 17, 92, 99
• GCD of 40, 21, 12, 99

1. What is the GCD of 84, 54, 18, 14?

GCD of 84, 54, 18, 14 is 2

2. Where do I get the detailed procedure to find GCD of 84, 54, 18, 14?

You can find a detailed procedure to find GCD of 84, 54, 18, 14 on our page.

3. How to find GCD of 84, 54, 18, 14 on a calculator?

You can find the GCD of 84, 54, 18, 14 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.