# Count numbers from range whose prime factors are only 2 and 3

Given two positive integers **L** and **R**, the task is to count the elements from the range **[L, R]** whose prime factors are only **2** and **3**.**Examples:**

Input:L = 1, R = 10Output:6

2 = 2

3 = 3

4 = 2 * 2

6 = 2 * 3

8 = 2 * 2 * 2

9 = 3 * 3Input:L = 100, R = 200Output:5

**Approach:** Start a loop from **L** to **R** and for every element **num**:

- While
**num**is divisible by**2**, divide it by**2**. - While
**num**is divisible by**3**, divide it by**3**. - If
**num = 1**then increment the**count**as**num**has only**2**and**3**as its prime factors.

Print the **count** in the end.

Below is the implementation of the above approach:

## C++

`// C++ program to count the numbers within a range` `// whose prime factors are only 2 and 3` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to count the number within a range` `// whose prime factors are only 2 and 3` `int` `findTwoThreePrime(` `int` `l, ` `int` `r)` `{` ` ` `// Start with 2 so that 1 doesn't get counted` ` ` `if` `(l == 1)` ` ` `l++;` ` ` `int` `count = 0;` ` ` `for` `(` `int` `i = l; i <= r; i++) {` ` ` `int` `num = i;` ` ` `// While num is divisible by 2, divide it by 2` ` ` `while` `(num % 2 == 0)` ` ` `num /= 2;` ` ` `// While num is divisible by 3, divide it by 3` ` ` `while` `(num % 3 == 0)` ` ` `num /= 3;` ` ` `// If num got reduced to 1 then it has` ` ` `// only 2 and 3 as prime factors` ` ` `if` `(num == 1)` ` ` `count++;` ` ` `}` ` ` `return` `count;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `l = 1, r = 10;` ` ` `cout << findTwoThreePrime(l, r);` ` ` `return` `0;` `}` |

## Java

`//Java program to count the numbers within a range` `// whose prime factors are only 2 and 3` `import` `java.io.*;` `class` `GFG {` ` ` `// Function to count the number within a range` `// whose prime factors are only 2 and 3` `static` `int` `findTwoThreePrime(` `int` `l, ` `int` `r)` `{` ` ` `// Start with 2 so that 1 doesn't get counted` ` ` `if` `(l == ` `1` `)` ` ` `l++;` ` ` `int` `count = ` `0` `;` ` ` `for` `(` `int` `i = l; i <= r; i++) {` ` ` `int` `num = i;` ` ` `// While num is divisible by 2, divide it by 2` ` ` `while` `(num % ` `2` `== ` `0` `)` ` ` `num /= ` `2` `;` ` ` `// While num is divisible by 3, divide it by 3` ` ` `while` `(num % ` `3` `== ` `0` `)` ` ` `num /= ` `3` `;` ` ` `// If num got reduced to 1 then it has` ` ` `// only 2 and 3 as prime factors` ` ` `if` `(num == ` `1` `)` ` ` `count++;` ` ` `}` ` ` `return` `count;` `}` `// Driver code` ` ` `public` `static` `void` `main (String[] args) {` ` ` `int` `l = ` `1` `, r = ` `10` `;` ` ` `System.out.println (findTwoThreePrime(l, r));` ` ` `}` `//This code is contributed by ajit ` `}` |

## Python3

`# Python3 program to count the numbers` `# within a range whose prime factors` `# are only 2 and 3` `# Function to count the number within` `# a range whose prime factors are only` `# 2 and 3` `def` `findTwoThreePrime(l, r) :` ` ` `# Start with 2 so that 1` ` ` `# doesn't get counted` ` ` `if` `(l ` `=` `=` `1` `) :` ` ` `l ` `+` `=` `1` ` ` `count ` `=` `0` ` ` `for` `i ` `in` `range` `(l, r ` `+` `1` `) :` ` ` `num ` `=` `i` ` ` `# While num is divisible by 2,` ` ` `# divide it by 2` ` ` `while` `(num ` `%` `2` `=` `=` `0` `) :` ` ` `num ` `/` `/` `=` `2` `;` ` ` `# While num is divisible by 3,` ` ` `# divide it by 3` ` ` `while` `(num ` `%` `3` `=` `=` `0` `) :` ` ` `num ` `/` `/` `=` `3` ` ` `# If num got reduced to 1 then it has` ` ` `# only 2 and 3 as prime factors` ` ` `if` `(num ` `=` `=` `1` `) :` ` ` `count ` `+` `=` `1` ` ` `return` `count` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `l ` `=` `1` ` ` `r ` `=` `10` ` ` ` ` `print` `(findTwoThreePrime(l, r))` ` ` `# This code is contributed by Ryuga` |

## C#

`// C# program to count the numbers` `// within a range whose prime factors` `// are only 2 and 3` `using` `System;` `class` `GFG` `{` ` ` `// Function to count the number` `// within a range whose prime` `// factors are only 2 and 3` `static` `int` `findTwoThreePrime(` `int` `l, ` `int` `r)` `{` ` ` `// Start with 2 so that 1` ` ` `// doesn't get counted` ` ` `if` `(l == 1)` ` ` `l++;` ` ` `int` `count = 0;` ` ` `for` `(` `int` `i = l; i <= r; i++)` ` ` `{` ` ` `int` `num = i;` ` ` `// While num is divisible by 2,` ` ` `// divide it by 2` ` ` `while` `(num % 2 == 0)` ` ` `num /= 2;` ` ` `// While num is divisible by 3,` ` ` `// divide it by 3` ` ` `while` `(num % 3 == 0)` ` ` `num /= 3;` ` ` `// If num got reduced to 1 then it ` ` ` `// has only 2 and 3 as prime factors` ` ` `if` `(num == 1)` ` ` `count++;` ` ` `}` ` ` `return` `count;` `}` `// Driver code` `static` `public` `void` `Main ()` `{` ` ` `int` `l = 1, r = 10;` ` ` `Console.WriteLine(findTwoThreePrime(l, r));` `}` `}` `// This code is contributed by akt_mit` |

## PHP

`<?php` `// PHP program to count the numbers` `// within a range whose prime factors` `// are only 2 and 3` `// Function to count the number` `// within a range whose prime` `// factors are only 2 and 3` `function` `findTwoThreePrime(` `$l` `, ` `$r` `)` `{` ` ` `// Start with 2 so that 1` ` ` `// doesn't get counted` ` ` `if` `(` `$l` `== 1)` ` ` `$l` `++;` ` ` `$count` `= 0;` ` ` `for` `(` `$i` `= ` `$l` `; ` `$i` `<= ` `$r` `; ` `$i` `++)` ` ` `{` ` ` `$num` `= ` `$i` `;` ` ` `// While num is divisible by 2,` ` ` `// divide it by 2` ` ` `while` `(` `$num` `% 2 == 0)` ` ` `$num` `/= 2;` ` ` `// While num is divisible by 3,` ` ` `// divide it by 3` ` ` `while` `(` `$num` `% 3 == 0)` ` ` `$num` `/= 3;` ` ` `// If num got reduced to 1 then it has` ` ` `// only 2 and 3 as prime factors` ` ` `if` `(` `$num` `== 1)` ` ` `$count` `++;` ` ` `}` ` ` `return` `$count` `;` `}` `// Driver code` `$l` `= 1;` `$r` `= 10;` `echo` `findTwoThreePrime(` `$l` `, ` `$r` `);` ` ` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` ` ` `// Javascript program to count the numbers` ` ` `// within a range whose prime factors` ` ` `// are only 2 and 3` ` ` ` ` `// Function to count the number` ` ` `// within a range whose prime` ` ` `// factors are only 2 and 3` ` ` `function` `findTwoThreePrime(l, r)` ` ` `{` ` ` `// Start with 2 so that 1` ` ` `// doesn't get counted` ` ` `if` `(l == 1)` ` ` `l++;` ` ` `let count = 0;` ` ` `for` `(let i = l; i <= r; i++)` ` ` `{` ` ` `let num = i;` ` ` `// While num is divisible by 2,` ` ` `// divide it by 2` ` ` `while` `(num % 2 == 0)` ` ` `num = parseInt(num / 2, 10);` ` ` `// While num is divisible by 3,` ` ` `// divide it by 3` ` ` `while` `(num % 3 == 0)` ` ` `num = parseInt(num / 3, 10);` ` ` `// If num got reduced to 1 then it ` ` ` `// has only 2 and 3 as prime factors` ` ` `if` `(num == 1)` ` ` `count++;` ` ` `}` ` ` `return` `count;` ` ` `}` ` ` ` ` `let l = 1, r = 10;` ` ` `document.write(findTwoThreePrime(l, r));` ` ` `</script>` |

**Time Complexity: **O((r-l)*log2(r-l))

**Auxiliary Space:** O(1), since no extra space has been taken.

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