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# Smallest number to multiply to convert floating point to natural

• Difficulty Level : Medium
• Last Updated : 22 Oct, 2021

Given a positive floating point number n, the task is to find the smallest integer k, such that when we multiply k with n, we get a natural number.
Examples:

```Input : 30.25
Output : 4
30.25 * 4 = 321, there is no number less than 4
which can convert 30.25 into natural number.

Input : 5.5
Output : 2
5.5 * 2 = 11, there is no number less than 2
which can convert 5.5 into natural number.

Input : 5.33
Output : 100```

The idea is to convert given floating point number into a fraction (not necessarily in reduced form) and find the GCD of numerator and denominator. For example, if input floating point number is 30.25, we convert into fraction as 3025/100. This can be easily done by finding the position of dot.
Finally to get the answer, we divide the denominator of the converted fraction by GCD of denominator and numerator. For example, GCD of 3025 and 100 is 25. We divide 100 by 25 and get the answer as 4.
Below is implementation of this approach:

## C++

 `// C++ program to find the smallest number to multiply``// to convert a floating point number into natural number.``#include``using` `namespace` `std;` `// Finding GCD of two number``int` `gcd(``int` `a, ``int` `b)``{``    ``if` `(b == 0)``        ``return` `a;``    ``return` `gcd(b, a%b);``}` `// Returns smallest integer k such that k * str becomes``// natural. str is an input floating point number``int` `findnum(string &str)``{``    ``// Find size of string representing a``    ``// floating point number.``    ``int` `n = str.length();` `    ``// Below is used to find denominator in``    ``// fraction form.``    ``int` `count_after_dot = 0;` `    ``// Used to find value of count_after_dot``    ``bool` `dot_seen = ``false``;` `    ``// To find numerator in fraction form of``    ``// given number. For example, for 30.25,``    ``// numerator would be 3025.``    ``int` `num = 0;``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``if` `(str[i] != ``'.'``)``        ``{``            ``num = num*10 + (str[i] - ``'0'``);``            ``if` `(dot_seen == ``true``)``                ``count_after_dot++;``        ``}``        ``else``            ``dot_seen = ``true``;``    ``}` `    ``// If there was no dot, then number``    ``// is already a natural.``    ``if` `(dot_seen == ``false``)``    ``return` `1;` `    ``// Find denominator in fraction form. For example,``    ``// for 30.25, denominator is 100``    ``int` `dem = (``int``)``pow``(10, count_after_dot);` `    ``// Result is denominator divided by``    ``// GCD-of-numerator-and-denominator. For example, for``    ``// 30.25, result is 100 / GCD(3025,100) = 100/25 = 4``    ``return` `(dem / gcd(num, dem));``}` `// Driven Program``int` `main()``{``    ``string str = ``"5.125"``;``    ``cout << findnum(str) << endl;``    ``return` `0;``}`

## Java

 `// Java program to find the smallest number to multiply``// to convert a floating point number into natural number.``class` `GFG {``  ``// Finding GCD of two number``  ``static` `int` `gcd(``int` `a, ``int` `b) {``    ``if` `(b == ``0``)``      ``return` `a;``    ``return` `gcd(b, a % b);``  ``}` `  ``// Returns smallest integer k such that k * str becomes``  ``// natural. str is an input floating point number``  ``static` `int` `findnum(String str) {``    ``// Find size of string representing a``    ``// floating point number.``    ``int` `n = str.length();` `    ``// Below is used to find denominator in``    ``// fraction form.``    ``int` `count_after_dot = ``0``;` `    ``// Used to find value of count_after_dot``    ``boolean` `dot_seen = ``false``;` `    ``// To find numerator in fraction form of``    ``// given number. For example, for 30.25,``    ``// numerator would be 3025.``    ``int` `num = ``0``;``    ``for` `(``int` `i = ``0``; i < n; i++) {``      ``if` `(str.charAt(i) != ``'.'``) {``        ``num = num * ``10` `+ (str.charAt(i) - ``'0'``);``        ``if` `(dot_seen == ``true``)``          ``count_after_dot++;``      ``} ``else``        ``dot_seen = ``true``;``    ``}` `    ``// If there was no dot, then number``    ``// is already a natural.``    ``if` `(dot_seen == ``false``)``      ``return` `1``;` `    ``// Find denominator in fraction form. For example,``    ``// for 30.25, denominator is 100``    ``int` `dem = (``int``)Math.pow(``10``, count_after_dot);` `    ``// Result is denominator divided by``    ``// GCD-of-numerator-and-denominator. For example, for``    ``// 30.25, result is 100 / GCD(3025, 100) = 100/25 = 4``    ``return` `(dem / gcd(num, dem));``  ``}` `  ``// Driver code``  ``public` `static` `void` `main(String[] args) {``    ``String str = ``"5.125"``;``    ``System.out.print(findnum(str));``  ``}``}``// This code is contributed by Anant Agarwal.`

## Python

 `# Python program to find the smallest number to multiply``# to convert a floating point number into natural number.``# Finding GCD of two number``import` `math``def` `gcd(a, b):` `    ``if` `(b ``=``=` `0``):``        ``return` `a``    ``return` `gcd(b, a``%``b)`` ` `# Returns smallest integer k such that k * str becomes``# natural. str is an input floating point number``def` `findnum(``str``):``    ` `    ``# Find size of string representing a``    ``# floating point number.``    ``n ``=` `len``(``str``)``    ``# Below is used to find denominator in``    ``# fraction form.``    ``count_after_dot ``=` `0`` ` `    ``# Used to find value of count_after_dot``    ``dot_seen ``=` `0`` ` `    ``# To find numerator in fraction form of``    ``# given number. For example, for 30.25,``    ``# numerator would be 3025.``    ``num ``=` `0``    ``for` `i ``in` `range``(n):``        ``if` `(``str``[i] !``=` `'.'``):``            ``num ``=` `num``*``10` `+` `int``(``str``[i])``            ``if` `(dot_seen ``=``=` `1``):``                ``count_after_dot ``+``=` `1``        ``else``:``            ``dot_seen ``=` `1`` ` `    ``# If there was no dot, then number``    ``# is already a natural.``    ``if` `(dot_seen ``=``=` `0``):``       ``return` `1`` ` `    ``# Find denominator in fraction form. For example,``    ``# for 30.25, denominator is 100``    ``dem ``=` `int``(math.``pow``(``10``, count_after_dot))`` ` `    ``# Result is denominator divided by``    ``# GCD-of-numerator-and-denominator. For example, for``    ``# 30.25, result is 100 / GCD(3025,100) = 100/25 = 4``    ``return` `(dem ``/` `gcd(num, dem))`` ` `# Driver Program` `str` `=` `"5.125"``print` `findnum(``str``)` `# Contributed by: Afzal Ansari`

## C#

 `// C# program to find the smallest``// number to multiply to convert a``// floating point number into``// natural number.``using` `System;` `class` `GFG {``    ` `// Finding GCD of two number``static` `int` `gcd(``int` `a, ``int` `b)``{``    ``if` `(b == 0)``    ``return` `a;``    ``return` `gcd(b, a % b);``}` `// Returns smallest integer k``// such that k * str becomes``// natural. str is an input``// floating point number``static` `int` `findnum(String str)``{` `    ``// Find size of string representing``    ``// a floating point number.``    ``int` `n = str.Length;` `    ``// Below is used to find denominator``    ``// in fraction form.``    ``int` `count_after_dot = 0;` `    ``// Used to find value of count_after_dot``    ``bool` `dot_seen = ``false``;` `    ``// To find numerator in fraction form of``    ``// given number. For example, for 30.25,``    ``// numerator would be 3025.``    ``int` `num = 0;``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``if` `(str[i] != ``'.'``)``        ``{``            ``num = num * 10 + (str[i] - ``'0'``);``            ``if` `(dot_seen == ``true``)``            ``count_after_dot++;``        ``}``        ``else``            ``dot_seen = ``true``;``    ``}` `    ``// If there was no dot, then``    ``// number is already a natural.``    ``if` `(dot_seen == ``false``)``    ``return` `1;` `    ``// Find denominator in fraction form.``    ``// For example, for 30.25,``    ``// denominator is 100``    ``int` `dem = (``int``)Math.Pow(10, count_after_dot);` `    ``// Result is denominator divided by``    ``// GCD-of-numerator-and-denominator.``    ``// For example, for 30.25, result is``    ``// 100 / GCD(3025, 100) = 100/25 = 4``    ``return` `(dem / gcd(num, dem));``}` `// Driver code``public` `static` `void` `Main()``{``    ``String str = ``"5.125"``;``    ``Console.Write(findnum(str));``}``}` `// This code is contributed by Nitin Mittal.`

## PHP

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## Javascript

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Output:

`8`

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