Bash Script to Check Perfect Number with Output

Use a Bash script that sums all divisors of a number except itself and compares the sum to the number with code like: sum=0; for ((i=1; i.

Examples

Input6

Output6 is perfect

Input28

Output28 is perfect

Input10

Output10 is not perfect

How to Think About It

To check if a number is perfect, find all its divisors except itself by checking which numbers divide it evenly using the modulo operator. Add these divisors together and compare the sum to the original number. If they match, the number is perfect.

Algorithm

1

Get the input number.

2

Initialize a sum variable to zero.

3

Loop from 1 to one less than the number.

4

For each number, check if it divides the input number evenly.

5

If yes, add it to the sum.

6

After the loop, compare the sum to the input number and print if it is perfect or not.

Code

bash

read -p "Enter a number: " num
sum=0
for ((i=1; i<num; i++)); do
  if (( num % i == 0 )); then
    sum=$((sum + i))
  fi
done
if (( sum == num )); then
  echo "$num is perfect"
else
  echo "$num is not perfect"
fi

Output

Enter a number: 6
6 is perfect

Dry Run

Let's trace the number 6 through the code

1

Initialize sum

sum=0

2

Loop i from 1 to 5

Check divisors: i=1,2,3,4,5

3

Add divisors to sum

i=1 divides 6, sum=1; i=2 divides 6, sum=3; i=3 divides 6, sum=6; i=4 no; i=5 no

4

Compare sum to number

sum=6 equals num=6, so 6 is perfect

i	num % i	sum
1	0	1
2	0	3
3	0	6
4	2	6
5	1	6

Why This Works

Step 1: Find divisors

The script uses num % i == 0 to find numbers that divide the input without remainder.

Step 2: Sum divisors

It adds all such divisors to sum to get the total of proper divisors.

Step 3: Check perfection

If the sum equals the original number, the number is perfect, so it prints the result.

Alternative Approaches

Using a while loop

bash

read -p "Enter a number: " num
sum=0
i=1
while (( i < num )); do
  if (( num % i == 0 )); then
    sum=$((sum + i))
  fi
  ((i++))
done
if (( sum == num )); then
  echo "$num is perfect"
else
  echo "$num is not perfect"
fi

This uses a while loop instead of for; functionally the same but some prefer while for clarity.

Using a function

bash

is_perfect() {
  local num=$1
  local sum=0
  for ((i=1; i<num; i++)); do
    if (( num % i == 0 )); then
      sum=$((sum + i))
    fi
  done
  [[ $sum -eq $num ]]
}
read -p "Enter a number: " n
if is_perfect "$n"; then
  echo "$n is perfect"
else
  echo "$n is not perfect"
fi

Encapsulates logic in a function for reuse and cleaner main code.

Complexity: O(n) time, O(1) space

Time Complexity

The script loops from 1 to n-1, so it runs in linear time O(n).

Space Complexity

Only a few variables are used, so space complexity is constant O(1).

Which Approach is Fastest?

All approaches use similar loops; using a function or while loop does not affect time complexity but may improve readability.

Approach	Time	Space	Best For
For loop	O(n)	O(1)	Simple and clear scripts
While loop	O(n)	O(1)	Preference for while syntax
Function encapsulation	O(n)	O(1)	Reusable and modular code