GCD of 420, 192, 312 Calculator
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Online GCD Calculator is useful to find the GCD of 420, 192, 312 quickly. Get the easiest ways to solve the greatest common divisor of 420, 192, 312 i.e 12 in different methods as follows.
Given Input numbers are 420, 192, 312
In the factoring method, we have to find the divisors of all numbers
Divisors of 420 :
The positive integer divisors of 420 that completely divides 420 are.
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
Divisors of 192 :
The positive integer divisors of 192 that completely divides 192 are.
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192
Divisors of 312 :
The positive integer divisors of 312 that completely divides 312 are.
1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
GCD of numbers is the greatest common divisor
So, the GCD (420, 192, 312) = 12.
Given numbers are 420, 192, 312
The list of prime factors of all numbers are
Prime factors of 420 are 2 x 2 x 3 x 5 x 7
Prime factors of 192 are 2 x 2 x 2 x 2 x 2 x 2 x 3
Prime factors of 312 are 2 x 2 x 2 x 3 x 13
The highest common occurrence is 22 x 31
Therefore, GCD of 420, 192, 312 is 12.
Steps to Calculate GCD of 420, 192, 312 using LCM Formula
Given numbers are 420, 192, 312
GCD of 2 numbers formula is GCD(a, b) = ( a x b) / LCM(a, b)
Apply this formula for all numbers.
Step1:
LCM(420, 192) = 6720
GCD(420, 192) = ( 420 x 192 ) / 6720
= 420 / 192
= 420
Step2:
LCM(12, 312) = 312
GCD(12, 312) = ( 12 x 312 ) / 312
= 12 / 312
= 12
So, Greatest Common Divisor of 420, 192, 312 is 12
GCD of Numbers Calculation Examples
Here are some samples of GCD of Numbers calculations.
Greatest Common Divisor of 420, 192, 312
Given numbers are 420, 192, 312
The greatest common divisor of numbers 420, 192, 312 can be found in various methods such as the LCM formula, factoring, and prime factorization. The GCD of numbers 420, 192, 312 is 12.
FAQs on GCD of 420, 192, 312 Calculator
1. What is the GCD of 420, 192, 312?
GCD of given numbers 420, 192, 312 is 12
2. How to calculate the greatest common divisor of 420, 192, 312?
We can find the highest common divisor of 420, 192, 312 easily using the prime factorization method. Just list the prime factors of all numbers and pick the highest common factor which is the GCD of 420, 192, 312 i.e 12.
3. How can I use the GCD of 420, 192, 312Calculator?
Out the numbers 420, 192, 312 into the GCD calculator and hit the calculate button to get the greatest common divisor as result.