Theory:

Finding the finding HCF using factors or repeated subtraction method is easy only for the small numbers. But it becomes tedious for larger numbers to find factors of the given numbers.
 
In that case, alternatively, we have some more methods to find HCF. Here we will learn one of the vital methods to find HCF; that method is known as the repeated division method.
 
Apply the below step by step theory with example to find the HCF by repeated division method.
Example:
Consider the two numbers 120 and 45.
 
Step 1: Divide the larger number by the smaller number.
 
Take the larger number 120 as dividend and smaller number 45 as divisor.
 
If we divide it we get the remainder as 30.
 
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Step 2: The remainder from Step -\(1\) becomes the new divisor, and divisor of Step -\(1\) becomes the new dividend.
 
From the Step -\(1\), we obtained 30 as remainder. Therefore, in the next step it becomes new divisor and 45 will become as the new divisor. Now if we divide it we get the remainder as 15.
 
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Step 3: We should repeat this division process till remainder becomes zero. When remainder is zero, the divisor of the last division is the required HCF.
 
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Hence, the HCF of 120 and 45 is 15.
We can apply the above method to find the HCF of two numbers. But how you calculate the HCF of three number?
 
Now we see how to find the HCF of three numbers with an example.
Example:
Find the HCF of \(34\), \(24\), \(16\).
 
Solution:
 
First we take the largest number \(32\) as dividend and smallest value \(16\) as divisor.
 
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Now we take remaining value \(24\) as dividend and \(16\) Common factor of \((\)\(16\), \(32\)\()\) as divisor.
 
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Therefore, the HCF of \((\)\(34\), \(24\), \(16\)\()\) is \(8\).