Check Perfect Number, Armstrong Number or Palindrome

AIM

To write Python programs that determine whether a number is a perfect number, an Armstrong number, or a palindrome.

ALGORITHM

Perfect Number Algorithm:

1. Start
2. Input a number n
3. Initialize sum = 0
4. For i from 1 to n-1:
5. If n % i == 0, then sum = sum + i
6. If sum == n, then it's a perfect number
7. Else, it's not a perfect number
8. Stop

Armstrong Number Algorithm:

1. Start
2. Input a number n
3. Count the number of digits
4. Initialize sum = 0
5. For each digit in the number:
6. Extract the digit and raise it to the power of number of digits
7. Add to sum
8. If sum equals original number, it's Armstrong
9. Stop

Palindrome Algorithm:

1. Start
2. Input a number n
3. Initialize reverse = 0
4. Store original number in temp
5. While n != 0:
6. Extract last digit
7. reverse = reverse * 10 + last_digit
8. n = n // 10
9. If temp == reverse, it's palindrome
10. Stop

PROGRAMS

Program 1: Perfect Number Check

# Determine whether a number is a perfect number
n = int(input("Enter any number: "))
sum = 0
i = 1

for i in range(1, n):
    if(n % i == 0):
        sum = sum + i

if (n == sum):
    print("The number is a Perfect number!")
else:
    print("The number is not a Perfect number!")

Program 2: Armstrong Number Check

# Finding Armstrong Number
n1 = int(input("Enter any number: "))
temp = num = n1
no_of_digits = 0

# Count number of digits
while(num != 0):
    no_of_digits += 1
    num = int(num / 10)

print("No of digits is:", no_of_digits)

# Sum of the digits power raise to no of digits
sum = 0
while(n1 != 0):
    last_digit = n1 % 10
    sum += (last_digit ** no_of_digits)
    n1 = int(n1 / 10)

# Checking Armstrong Number
if(sum == temp):
    print("Number is Armstrong number")
else:
    print("Number is Not Armstrong number")

Program 3: Palindrome Check

# Finding Palindrome or Not
n = int(input("Enter the Number: "))
rev = 0
temp = n

while(n != 0):
    last_digit = n % 10
    rev = rev * 10 + last_digit
    n = n // 10

if(temp == rev):
    print("It is Palindrome Number")
else:
    print("It is not a Palindrome Number")

OUTPUT

Perfect Number Output:

Armstrong Number Output:

Palindrome Output:

CONCLUSION

Thus, the given program was successfully executed and the output was verified as per the expected result.

VIVA QUESTIONS

1. What is a perfect number? Give examples.

   A perfect number is a positive integer that is equal to the sum of its proper positive divisors (excluding itself). Examples: 6 (1+2+3=6), 28 (1+2+4+7+14=28), 496, 8128.

2. How do you calculate if 371 is an Armstrong number?

   371 has 3 digits. Calculate: 3³ + 7³ + 1³ = 27 + 343 + 1 = 371. Since the sum equals the original number, 371 is an Armstrong number.

3. What is the difference between // and / operators in Python?

   // is floor division (returns integer quotient), while / is true division (returns float). For digit extraction, we use // to get integer results.

4. Why do we use modulo operator (%) in these programs?

   The modulo operator is used to: find divisors (n%i==0), extract last digit (n%10), and check divisibility conditions.

5. How would you modify the palindrome program to work with strings?

   For strings, we can use string slicing: if string == string[::-1] or compare characters from both ends using loops.

6. What happens if we input 0 or negative numbers?

   Perfect numbers are defined for positive integers only. For 0 or negative numbers, we should add input validation to handle these cases appropriately.

7. Can a single-digit number be an Armstrong number?

   Yes, all single-digit numbers (1-9) are Armstrong numbers because each digit raised to the power 1 equals itself.

8. How can we optimize the perfect number checking algorithm?

   We can optimize by checking divisors only up to √n, and for each divisor i found, also add n/i to the sum (if i ≠ n/i and n/i ≠ n).