# C Program to Reverse a Number Using Recursion

• Write a C program to reverse digits of a number using recursion
• Write a C program to reverse a number using recursion

Reversing the digits of a number means reversing the sequence of digits in a number. After reversing, least significant digit will become most significant digit of number and most significant digit becomes least significant digit and so on.
Let the total number of digits in a number is N. So a digit at ith position from left will become ith digit from right or N-i+1th digit from left.

##### For Example
Befor reverse : 25346
After reverse : 64352

Algorithm to reverse a number using recursion
• N%10 returns the last digit(least significant) of N. For Example : 354%10 = 4.

• N/10 return the number after removing least significant digit of N(rightmost digit of N). For Example: 2345/10 = 234.

• log10(N) + 1 returns the number of digits in N. log10(N) is logarithm of N with base 10. For Example: log10(2311) + 1 = 4.

• Let getReversedNumber(N) is a function, which returns reverse of N. Then, we can use recursion to reverse the digits if a number using below mention recursive equation.
• getReversedNumber(N) = (N%10)X pow(10, (log10(N/10) + 1)) + getReversedNumber(N/10)
##### For Example
• getReversedNumber(8645) = lastDigitOf(8645) x power(10, numberOfDigits(864)) + getReversedNumber(864)
• getReversedNumber(8645) = lastDigitOf(8645) x 1000 + getReversedNumber(864)
• getReversedNumber(8645) = 5x1000 + getReversedNumber(864)
• getReversedNumber(8645) = 5x1000 + 468
• getReversedNumber(8645) = 5468
• ## C program to reverse the digits of a number recursively

This program first take an integer as input form user, then reverse it's digits using modulus(%), division(/), multiplication(*) and logarithmic function inside a recursive function. After reversing it prints the reversed number.

```/*
* C Program to reverse the digits of a number using recursion
*/
#include <stdio.h>
#include <conio.h>
#include <math.h>

int getReversedNumber(int number);
int main(){
int number, reverse = 0;
printf("Enter a number\n");
scanf("%d", &number);

reverse = getReversedNumber(number);

printf("Reversed number : %d\n", reverse);
getch();
return 0;
}

/*
* Function to reverse the digits of a number
*/
int getReversedNumber(int number){
int lastDigit, numberOfDigits, sign = 1;

if(number < 0){
number = number * -1;
sign = -1;
}
if(number < 10)
return number*sign;

lastDigit = number % 10;
number = number / 10;
/* log10(number) + 1 gives number of digits in number */
numberOfDigits = log10(number) + 1;
/*
* for Example: getReversedNumber(1234) =
*        ((4*1000) + getReversedNumber(321))*1
*/
return (lastDigit*pow(10,numberOfDigits) +
getReversedNumber(number))*sign;
}
```

Program Output
```Enter a number
6542
Reversed number : 2456
```

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