Bash Script to Find Factors of a Number

Use a Bash script with a loop from 1 to the number and check if number % i == 0 to print all factors; for example: for ((i=1; i<=num; i++)); do if (( num % i == 0 )); then echo $i; fi; done.

Examples

Input6

Output1 2 3 6

Input13

Output1 13

Input1

Output1

How to Think About It

To find factors of a number, think of checking every number from 1 up to that number. If dividing the number by this candidate leaves no remainder, it means the candidate is a factor. We print all such candidates.

Algorithm

1

Get the input number.

2

Start a loop from 1 to the input number.

3

For each number in the loop, check if it divides the input number evenly (remainder zero).

4

If yes, print that number as a factor.

5

End the loop after reaching the input number.

Code

bash

#!/bin/bash
read -p "Enter a number: " num
for ((i=1; i<=num; i++)); do
  if (( num % i == 0 )); then
    echo $i
  fi
done

Output

Enter a number: 6
1
2
3
6

Dry Run

Let's trace the number 6 through the code

1

Start loop with i=1

Check if 6 % 1 == 0 → yes, print 1

2

Next i=2

Check if 6 % 2 == 0 → yes, print 2

3

Next i=3

Check if 6 % 3 == 0 → yes, print 3

i	6 % i	Is factor?
1	0	Yes
2	0	Yes
3	0	Yes
4	2	No
5	1	No
6	0	Yes

Why This Works

Step 1: Loop through numbers

The script loops from 1 to the input number to check every possible factor.

Step 2: Check divisibility

Using num % i == 0 checks if the remainder is zero, meaning i divides num exactly.

Step 3: Print factors

When a factor is found, it is printed immediately to show all factors one by one.

Alternative Approaches

Using while loop

bash

#!/bin/bash
read -p "Enter a number: " num
i=1
while [ $i -le $num ]; do
  if (( num % i == 0 )); then
    echo $i
  fi
  ((i++))
done

This uses a while loop instead of for; functionally similar but shows different loop style.

Optimized up to sqrt(num)

bash

#!/bin/bash
read -p "Enter a number: " num
for ((i=1; i*i<=num; i++)); do
  if (( num % i == 0 )); then
    echo $i
    if (( i != num / i )); then
      echo $((num / i))
    fi
  fi
done

This prints factors in pairs and only loops up to the square root, improving efficiency for large numbers.

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

Time Complexity

The script checks every number from 1 to n, so it runs in linear time O(n).

Space Complexity

Uses constant extra space O(1) as it only stores counters and prints results immediately.

Which Approach is Fastest?

The optimized sqrt(n) approach reduces time to O(√n), which is faster for large numbers but slightly more complex.

Approach	Time	Space	Best For
Simple for loop	O(n)	O(1)	Small to medium numbers
While loop	O(n)	O(1)	Same as for loop, different style
Optimized sqrt loop	O(√n)	O(1)	Large numbers, better performance