Java Program to Check if a Number is a Multiple of 5 Without Using / and % Operators

Given a number n. The task is to check if a number is a multiple of 5 without using the division (/) or modulus (%) operators.

Example 1:

Input: 30

Output: 30 is a multiple of 5: true

Explanation: The last digit of 30 is 0, so it is a multiple of 5.

Example 2:

Input: 17

Output: 17 is a multiple of 5: false

Explanation: The last digit of 17 is 7, which is not 0 or 5, so it's not a multiple of 5.

Example 3:

Input: 125

Output: 125 is a multiple of 5: true

Explanation: The last digit of 125 is 5, so it is a multiple of 5.

Approach 1: Using Repeated Subtraction

The approach determines whether a given number is a multiple of 5 by repeatedly subtracting 5 from it. If the number eventually reduces to 0, it is a multiple of 5; otherwise, it is not.

Algorithm

Step 1: Convert the number to its absolute value to handle negative numbers.

Step 2: Repeatedly subtract 5 from the number until it is less than 5.

Step 3: If the remaining value is 0, return true (it is a multiple of 5); otherwise, return false.

Output:

 25 is a multiple of 5: true 

Complexity

Time Complexity: The time complexity of a program is O(n). Because we repeatedly subtract 5, so for a large n, the loop runs approximately n/5 times.

Space Complexity: The space complexity of a program is O(1). Because no extra space is used apart from a few integer variables.

Approach 2: Using Multiplication and Subtraction

The approach checks if a number is a multiple of 5 by iterating from 0 and multiplying by 5 until we either reach the given number or surpass it. If we find a match, the number is a multiple of 5; otherwise, it is not.

Algorithm

Step 1: Take the absolute value of the number to handle negative cases.

Step 2: Initialize x = 0.

Step 3: Use a loop to compute 5 * x and check if it matches n:

Step 3.1: If 5 * x == n, return true.

Step 3.2: If 5 * x exceeds n, return false.

Step 3.3: Otherwise, increment x and continue.

Output:

 20 is a multiple of 5: true 

Complexity

Time Complexity: The time complexity of a program is O(n). Because we iterate a loop to compute.

Space Complexity: The space complexity of a program is O(1). Because no extra space is used apart from a few integer variables.

Approach 3: Convert Number to String and Check Last Digit

The approach converts the given number into a string and checks if the last digit is 0 or 5. Since numbers that are multiples of 5 always end in 0 or 5.

Algorithm

Step 1: Convert the number to its absolute value (to handle negatives).

Step 2: Convert the absolute number to a string.

Step 3: Extract the last digit using charAt(length - 1).

Step 4: If the last digit is '0' or '5', return true; otherwise, return false.

Output:

 20 is a multiple of 5: true 

Complexity

Time Complexity: The time complexity of a program is O(n). Because we use a string conversion and last-digit checking are quick operations.

Space Complexity: The space complexity of a program is O(1). Because only a string and a character variable are used.