In this tutorial, we will learn how to check if a number is a perfect number in Swift. We will understand the concept of a perfect number, write an algorithm to determine it, and implement the solution step by step with a complete Swift program and output.

What is a Perfect Number?

A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself). For example:

  • 6 is a perfect number because its divisors (excluding itself) are 1, 2, 3, and their sum is 1 + 2 + 3 = 6.
  • 28 is a perfect number because its divisors (excluding itself) are 1, 2, 4, 7, 14, and their sum is 1 + 2 + 4 + 7 + 14 = 28.
  • 12 is not a perfect number because its divisors (excluding itself) are 1, 2, 3, 4, 6, and their sum is 1 + 2 + 3 + 4 + 6 = 16.

We will now write an algorithm to determine if a number is a perfect number.

Algorithm to Check Perfect Number

To check if a number is a perfect number, follow these steps:

  1. Take a positive integer as input.
  2. Initialize a variable sum to 0 to store the sum of divisors.
  3. Iterate from 1 to number / 2 (inclusive) to find all divisors:
    1. Check if the current number divides the input number without a remainder.
    2. If yes, add the current number to sum.
  4. After the loop, compare sum with the original number:
  5. If they are equal, the number is a perfect number; otherwise, it is not.

This algorithm ensures that only proper divisors are considered, and the calculation is efficient by limiting the iteration to half of the number.

Step-by-Step Implementation in Swift

Let’s implement the algorithm in Swift step by step.

1 Writing function to check Perfect Number

Create a function to initialize the sum variable and iterate through potential divisors:

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func isPerfectNumber(_ number: Int) -> Bool {
    if number <= 1 {
        return false // Perfect numbers must be greater than 1
    }
    
    var sum = 0 // Initialize sum of divisors
    
    for i in 1...(number / 2) {
        if number % i == 0 {
            sum += i // Add the divisor to the sum
        }
    }
    
    return sum == number // Check if the sum equals the original number
}

Explanation:

if number <= 1: Ensures the number is greater than 1 because perfect numbers are positive integers.

for i in 1...(number / 2): Iterates through all potential divisors up to half the number.

if number % i == 0: Checks if i is a divisor of the number.

sum += i: Adds the divisor to the running total.

return sum == number: Compares the sum of divisors with the original number to determine if it is a perfect number.

2 Test the Function

Let’s test the function with some example inputs:

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// Test cases
print("6 is a perfect number: \(isPerfectNumber(6))")    // true
print("28 is a perfect number: \(isPerfectNumber(28))")  // true
print("12 is a perfect number: \(isPerfectNumber(12))")  // false
print("1 is a perfect number: \(isPerfectNumber(1))")    // false

The function correctly identifies whether the numbers are perfect numbers or not.

Complete Swift Program

Here’s the complete Swift program to find the sum of the digits of a number:

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import Foundation

// Function to check if a number is a perfect number
func isPerfectNumber(_ number: Int) -> Bool {
    if number <= 1 {
        return false // Perfect numbers must be greater than 1
    }
    
    var sum = 0 // Initialize sum of divisors
    
    for i in 1...(number / 2) {
        if number % i == 0 {
            sum += i // Add the divisor to the sum
        }
    }
    
    return sum == number // Check if the sum equals the original number
}

// Test cases
print("6 is a perfect number: \(isPerfectNumber(6))")    // true
print("28 is a perfect number: \(isPerfectNumber(28))")  // true
print("12 is a perfect number: \(isPerfectNumber(12))")  // false
print("1 is a perfect number: \(isPerfectNumber(1))")    // false

Output

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6 is a perfect number: true
28 is a perfect number: true
12 is a perfect number: false
1 is a perfect number: false

Screenshot from Xcode

Swift Program to Check Perfect Number