# C Program to convert a decimal number to an octal number

Last updated on September 24, 2020

The following is a C program to convert a decimal number to an octal number:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 /******************************************************* Program to convert a decimal number to an octal number ******************************************************/ #include // include stdio.h library #include // include math.h library int main(void) { long long num, oct = 0; int i = 0, rem; printf("Enter a decimal number: "); scanf("%lld", &num); while(num != 0) { rem = num % 8; // get the last digit oct = rem * (long long)pow(10, i++) + oct; num /= 8; // get the quotient } printf("0o"); printf("%lld", oct); return 0; // return 0 to operating system } 

Expected Output: 1st run:

 1 2 Enter a decimal number: 74 0o112 

2nd run:

 1 2 Enter a decimal number: 2545 0o4761 

## How it works #

To convert a decimal number to an octal number, we follow these steps:

Step 1: Divide the decimal number continuously by 8 and write the remainder on the right-hand side of the dividend. We repeat this process until we get the quotient 0.

Step 2: Write the remainders from bottom to top.

Let's take some examples:

Example 1: Convert decimal 125 to an octal number:

Step 1:

Quotient Remainder
125/8 15 5
15/8 1 7
1/2 0 1

Step 2:

$$\mathtt{125_{10} = 175_{8}}$$

Example 2: Convert decimal 500 to an octal number:

Step 1:

Quotient Remainder
500/8 62 4
62/8 7 6
1/2 0 7

Step 2:

$$\mathtt{500_{10} = 764_{8}}$$

The following table shows what happens at each iteration of the loop (assuming num = 74):

Iteration rem bin num i
After 1st iteration rem=74%8=2 oct=2*(10^0)+0=2 num=74/8=9 i=2
After 2nd iteration rem=9%8=1 oct=1*(10^1)+2=12 num=9/8=1 i=3
After 3rd iteration rem=1%8=1 oct=1*(10^2)+12=112 num=1/8=0 i=4