GCD of 345, 135, 84, 654 Calculator

Given Input numbers are 345, 135, 84, 654

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

Divisors of 345

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

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

Divisors of 135

List of positive integer divisors of 135 that divides 135 without a remainder.

1, 3, 5, 9, 15, 27, 45, 135

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 654

List of positive integer divisors of 654 that divides 654 without a remainder.

1, 2, 3, 6, 109, 218, 327, 654

Greatest Common Divisior

We found the divisors of 345, 135, 84, 654 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 345, 135, 84, 654 is 3.

Therefore, GCD of numbers 345, 135, 84, 654 is 3

Given Input Data is 345, 135, 84, 654

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

Prime Factorization of 345 is 3 x 5 x 23

Prime Factorization of 135 is 3 x 3 x 3 x 5

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

Prime Factorization of 654 is 2 x 3 x 109

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(345, 135) = 3105

GCD(345, 135) = ( 345 x 135 ) / 3105

GCD(345, 135) = 46575 / 3105

GCD(345, 135) = 15

Step2:

Here we consider the GCD from the above i.e. 15 as first number and the next as 84

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

LCM(15, 84) = 420

GCD(15, 84) = ( 15 x 84 ) / 420

GCD(15, 84) = 1260 / 420

GCD(15, 84) = 3

Step3:

Here we consider the GCD from the above i.e. 3 as first number and the next as 654

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

LCM(3, 654) = 654

GCD(3, 654) = ( 3 x 654 ) / 654

GCD(3, 654) = 1962 / 654

GCD(3, 654) = 3

GCD of 345, 135, 84, 654 is 3

Here are some samples of GCD of Numbers calculations.

• GCD of 454, 185, 98, 770
• GCD of 666, 526, 10, 136
• GCD of 408, 494, 29, 158
• GCD of 125, 841, 73, 935
• GCD of 820, 601, 98, 557

1. What is the GCD of 345, 135, 84, 654?

GCD of 345, 135, 84, 654 is 3

2. Where do I get the detailed procedure to find GCD of 345, 135, 84, 654?

You can find a detailed procedure to find GCD of 345, 135, 84, 654 on our page.

3. How to find GCD of 345, 135, 84, 654 on a calculator?

You can find the GCD of 345, 135, 84, 654 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.