Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Make use of GCD Calculator to determine the Greatest Common Divisor of 360, 708, 45, 240 i.e. 3 largest integer that divides all the numbers equally.
GCD of 360, 708, 45, 240 is 3
GCD(360, 708, 45, 240) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 360, 708, 45, 240 is 3
GCD(360, 708, 45, 240) = 3
Given Input numbers are 360, 708, 45, 240
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 708
List of positive integer divisors of 708 that divides 708 without a remainder.
1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
Divisors of 45
List of positive integer divisors of 45 that divides 45 without a remainder.
1, 3, 5, 9, 15, 45
Divisors of 240
List of positive integer divisors of 240 that divides 240 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
Greatest Common Divisior
We found the divisors of 360, 708, 45, 240 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 360, 708, 45, 240 is 3.
Therefore, GCD of numbers 360, 708, 45, 240 is 3
Given Input Data is 360, 708, 45, 240
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 708 is 2 x 2 x 3 x 59
Prime Factorization of 45 is 3 x 3 x 5
Prime Factorization of 240 is 2 x 2 x 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(360, 708) = 21240
GCD(360, 708) = ( 360 x 708 ) / 21240
GCD(360, 708) = 254880 / 21240
GCD(360, 708) = 12
Step2:
Here we consider the GCD from the above i.e. 12 as first number and the next as 45
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(12, 45) = 180
GCD(12, 45) = ( 12 x 45 ) / 180
GCD(12, 45) = 540 / 180
GCD(12, 45) = 3
Step3:
Here we consider the GCD from the above i.e. 3 as first number and the next as 240
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 240) = 240
GCD(3, 240) = ( 3 x 240 ) / 240
GCD(3, 240) = 720 / 240
GCD(3, 240) = 3
GCD of 360, 708, 45, 240 is 3
Here are some samples of GCD of Numbers calculations.
1. What is the GCD of 360, 708, 45, 240?
GCD of 360, 708, 45, 240 is 3
2. Where do I get the detailed procedure to find GCD of 360, 708, 45, 240?
You can find a detailed procedure to find GCD of 360, 708, 45, 240 on our page.
3. How to find GCD of 360, 708, 45, 240 on a calculator?
You can find the GCD of 360, 708, 45, 240 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.