C++ Program to calculate the Highest Common Factor

The highest Common Factor or Greatest Common Divisor are factors that are maximum and that can divide two or more values without generating any remainder. In this article, we shall discuss a few methods to perform HCF / GCD between two numbers in C++.

This is simply a mathematical solution and there are several algorithms present to find GCD. The Euclidean method to find GCD is common. The same algorithm we will use in iterative mode, and recursive mode.

Using Iterative method

The iterative solution for the Euclidean gcd finding algorithm is shown in the algorithm section.

Algorithm

• Take two numbers a and b as input.
• If a is 0, then return b.
• If b is 0, return a.
• While a and b are not the same, do.
  • If a > b, then a := a - b.
  • Otherwise b := b - a.
• End While.
• Return HCF as variable a.

Example

<div class="execute"></div><div class="code-mirror  language-cpp" contenteditable="plaintext-only" spellcheck="false" style="outline: none; overflow-wrap: break-word; overflow-y: auto; white-space: pre-wrap;"><span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span> <span class="token string"><iostream></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>

<span class="token keyword">int</span> <span class="token function">solve</span><span class="token punctuation">(</span> <span class="token keyword">int</span> x<span class="token punctuation">,</span> <span class="token keyword">int</span> y<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token keyword">if</span> <span class="token punctuation">(</span>x <span class="token operator">==</span> <span class="token number">0</span><span class="token punctuation">)</span>
      <span class="token keyword">return</span> y<span class="token punctuation">;</span>
   <span class="token keyword">else</span> <span class="token keyword">if</span> <span class="token punctuation">(</span>y <span class="token operator">==</span> <span class="token number">0</span><span class="token punctuation">)</span>
      <span class="token keyword">return</span> x<span class="token punctuation">;</span>
   <span class="token keyword">while</span> <span class="token punctuation">(</span>x <span class="token operator">!=</span> y<span class="token punctuation">)</span> <span class="token punctuation">{</span>
      <span class="token keyword">if</span> <span class="token punctuation">(</span>x <span class="token operator">></span> y<span class="token punctuation">)</span>
         x <span class="token operator">=</span> x <span class="token operator">-</span> y<span class="token punctuation">;</span>
      <span class="token keyword">else</span>
         y <span class="token operator">=</span> y <span class="token operator">-</span> x<span class="token punctuation">;</span>
   <span class="token punctuation">}</span>
   <span class="token keyword">return</span> x<span class="token punctuation">;</span>
<span class="token punctuation">}</span>

<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span> <span class="token keyword">int</span> argc<span class="token punctuation">,</span> <span class="token keyword">char</span><span class="token operator">*</span> argv<span class="token punctuation">[</span><span class="token punctuation">]</span> <span class="token punctuation">)<font color="#000000"> </font></span><span class="token punctuation">{</span>
   cout <span class="token operator"><<</span> <span class="token string">"HCF of two numbers 12 and 72 is: "</span> <span class="token operator"><<</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">12</span><span class="token punctuation">,</span> <span class="token number">72</span><span class="token punctuation">)</span> <span class="token operator"><<</span> endl<span class="token punctuation">;</span>
   cout <span class="token operator"><<</span> <span class="token string">"HCF of two numbers 18 and 13 is: "</span> <span class="token operator"><<</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">18</span><span class="token punctuation">,</span> <span class="token number">13</span><span class="token punctuation">)</span> <span class="token operator"><<</span>   endl<span class="token punctuation">;</span>
   cout <span class="token operator"><<</span> <span class="token string">"HCF of two numbers 117 and 96 is: "</span> <span class="token operator"><<</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">117</span><span class="token punctuation">,</span> <span class="token number">96</span><span class="token punctuation">)</span> <span class="token operator"><<</span> endl<span class="token punctuation">;</span>
   cout <span class="token operator"><<</span> <span class="token string">"HCF of two numbers 85 and 15 is: "</span> <span class="token operator"><<</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">85</span><span class="token punctuation">,</span> <span class="token number">15</span><span class="token punctuation">)</span> <span class="token operator"><<</span> endl<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</div><div class="output-wrapper"><div class="console-close"></div><div class="code-output"></div></div>

Output

HCF of two numbers 12 and 72 is: 12
HCF of two numbers 18 and 13 is: 1
HCF of two numbers 117 and 96 is: 3
HCF of two numbers 85 and 15 is: 5

Using Iterative method

The same Euclidean method can be implemented using the recursive method. Here we are describing the recursive method definition in the following algorithm.

Algorithm

• Define a function HCF that takes two numbers a and b.
• If a is 0, then return b
• Otherwise return HCF( b mod a, a)

Example

<div class="execute"></div><div class="code-mirror  language-cpp" contenteditable="plaintext-only" spellcheck="false" style="outline: none; overflow-wrap: break-word; overflow-y: auto; white-space: pre-wrap;"><span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span> <span class="token string"><iostream></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>

<span class="token keyword">int</span> <span class="token function">solve</span><span class="token punctuation">(</span> <span class="token keyword">int</span> x<span class="token punctuation">,</span> <span class="token keyword">int</span> y<span class="token punctuation">)</span> <span class="token punctuation">{</span>
   <span class="token keyword">if</span> <span class="token punctuation">(</span>x <span class="token operator">==</span> <span class="token number">0</span><span class="token punctuation">)</span>
      <span class="token keyword">return</span> y<span class="token punctuation">;</span>
   <span class="token keyword">return</span> <span class="token function">solve</span><span class="token punctuation">(</span> y <span class="token operator">%</span> x<span class="token punctuation">,</span> x <span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>

<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span> <span class="token keyword">int</span> argc<span class="token punctuation">,</span> <span class="token keyword">char</span><span class="token operator">*</span> argv<span class="token punctuation">[</span><span class="token punctuation">]</span> <span class="token punctuation">)<font color="#000000"> </font></span><span class="token punctuation">{</span>
   cout <span class="token operator"><<</span> <span class="token string">"HCF of two numbers 12 and 72 is: "</span> <span class="token operator"><<</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">12</span><span class="token punctuation">,</span> <span class="token number">72</span><span class="token punctuation">)</span> <span class="token operator"><<</span> endl<span class="token punctuation">;</span>
   cout <span class="token operator"><<</span> <span class="token string">"HCF of two numbers 18 and 13 is: "</span> <span class="token operator"><<</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">18</span><span class="token punctuation">,</span> <span class="token number">13</span><span class="token punctuation">)</span> <span class="token operator"><<</span> endl<span class="token punctuation">;</span>
   cout <span class="token operator"><<</span> <span class="token string">"HCF of two numbers 117 and 96 is: "</span> <span class="token operator"><<</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">117</span><span class="token punctuation">,</span> <span class="token number">96</span><span class="token punctuation">)</span> <span class="token operator"><<</span> endl<span class="token punctuation">;</span>
   cout <span class="token operator"><<</span> <span class="token string">"HCF of two numbers 85 and 15 is: "</span> <span class="token operator"><<</span> <span class="token function">solve</span><span class="token punctuation">(</span><span class="token number">85</span><span class="token punctuation">,</span> <span class="token number">15</span><span class="token punctuation">)</span> <span class="token operator"><<</span> endl<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</div><div class="output-wrapper"><div class="console-close"></div><div class="code-output"></div></div>

Output

HCF of two numbers 12 and 72 is: 12
HCF of two numbers 18 and 13 is: 1
HCF of two numbers 117 and 96 is: 3
HCF of two numbers 85 and 15 is: 5

Conclusion

Getting Highest Common Factor or Greatest Common Divisor is a very useful thing while solving different mathematical problems. The Euclidean method can be used to calculate the same. The same method can be applied iteratively as well as recursively. Here we have shown both of them. On the other hand, we can calculate GCD/HCF with the Least Common Multiplier (LCM). The GCD and LCM of two numbers are the same as the multiplication of these two numbers. So from that principle, if we know the LCM and the multiplication of these two numbers, the GCD can be calculated easily.