GCD of 21, 75, 42 Calculator
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 21, 75, 42 i.e. 3 largest integer that divides all the numbers equally.
GCD of 21, 75, 42 is 3
GCD(21, 75, 42) = 3
Ex: 10, 15, 20 (or) 24, 48, 96,45 (or) 78902, 89765, 12345
GCD of numbers 21, 75, 42 is 3
GCD(21, 75, 42) = 3
GCDof 21,75,42 is 3
Given Input numbers are 21, 75, 42
To find the GCD of numbers using factoring list out all the divisors of each number
Divisors of 21
List of positive integer divisors of 21 that divides 21 without a remainder.
1, 3, 7, 21
Divisors of 75
List of positive integer divisors of 75 that divides 75 without a remainder.
1, 3, 5, 15, 25, 75
Divisors of 42
List of positive integer divisors of 42 that divides 42 without a remainder.
1, 2, 3, 6, 7, 14, 21, 42
Greatest Common Divisior
We found the divisors of 21, 75, 42 . The biggest common divisior number is the GCD number.
So the Greatest Common Divisior 21, 75, 42 is 3.
Therefore, GCD of numbers 21, 75, 42 is 3
Given Input Data is 21, 75, 42
Make a list of Prime Factors of all the given numbers initially
Prime Factorization of 21 is 3 x 7
Prime Factorization of 75 is 3 x 5 x 5
Prime Factorization of 42 is 2 x 3 x 7
Highest common occurrences in the given inputs are 31
Multiplying them we get the GCD as 3
Finding GCD of 21, 75, 42 using LCM Formula
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(21, 75) = 525
GCD(21, 75) = ( 21 x 75 ) / 525
GCD(21, 75) = 1575 / 525
GCD(21, 75) = 3
Step2:
Here we consider the GCD from the above i.e. 3 as first number and the next as 42
The formula of GCD is GCD(a, b) = ( a x b) / LCM(a, b)
LCM(3, 42) = 42
GCD(3, 42) = ( 3 x 42 ) / 42
GCD(3, 42) = 126 / 42
GCD(3, 42) = 3
GCD of 21, 75, 42 is 3
GCD of Numbers Calculation Examples
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FAQs on GCD of numbers 21, 75, 42
1. What is the GCD of 21, 75, 42?
GCD of 21, 75, 42 is 3
2. Where do I get the detailed procedure to find GCD of 21, 75, 42?
You can find a detailed procedure to find GCD of 21, 75, 42 on our page.
3. How to find GCD of 21, 75, 42 on a calculator?
You can find the GCD of 21, 75, 42 by simply giving the inputs separated by commas and click on the calculate button to avail the Greatest Common Divisor in less time.