GCD of 360, 690, 174 Calculator

Given Input numbers are 360, 690, 174

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

Divisors of 360

List of positive integer divisors of 360 that divides 360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Divisors of 690

List of positive integer divisors of 690 that divides 690 without a remainder.

1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

Divisors of 174

List of positive integer divisors of 174 that divides 174 without a remainder.

1, 2, 3, 6, 29, 58, 87, 174

Greatest Common Divisior

We found the divisors of 360, 690, 174 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 360, 690, 174 is 6.

Therefore, GCD of numbers 360, 690, 174 is 6

Given Input Data is 360, 690, 174

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

Prime Factorization of 360 is 2 x 2 x 2 x 3 x 3 x 5

Prime Factorization of 690 is 2 x 3 x 5 x 23

Prime Factorization of 174 is 2 x 3 x 29

Highest common occurrences in the given inputs are 2¹ x 3¹

Multiplying them we get the GCD as 6

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(360, 690) = 8280

GCD(360, 690) = ( 360 x 690 ) / 8280

GCD(360, 690) = 248400 / 8280

GCD(360, 690) = 30

Step2:

Here we consider the GCD from the above i.e. 30 as first number and the next as 174

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

LCM(30, 174) = 870

GCD(30, 174) = ( 30 x 174 ) / 870

GCD(30, 174) = 5220 / 870

GCD(30, 174) = 6

GCD of 360, 690, 174 is 6

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1. What is the GCD of 360, 690, 174?

GCD of 360, 690, 174 is 6

2. Where do I get the detailed procedure to find GCD of 360, 690, 174?

You can find a detailed procedure to find GCD of 360, 690, 174 on our page.

3. How to find GCD of 360, 690, 174 on a calculator?

You can find the GCD of 360, 690, 174 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.