Print all Strong Numbers in Given List - Python

Last Updated : 08 Feb, 2025

The task of printing all Strong numbers from a given list in Python involves iterating through the list and checking each number based on its digit factorial sum. A Strong number is a number whose sum of the factorials of its digits equals the number itself. For example, given a list a = [145, 375, 100, 2, 10, 40585, 0], the goal is to identify and print numbers like 145 and 40585, where 1! + 4! + 5! = 145 and 4! + 0! + 5! + 8! + 5! = 40585.

Using precomputed factorials

In this method, we store the factorials of digits (0-9) in advance using a dictionary. This allows us to quickly check if a number is strong without recalculating factorials, making it the fastest approach.

Python

from math import factorial

# Precompute factorials for digits 0-9
fact = {i: factorial(i) for i in range(10)}

a = [145, 375, 100, 2, 10, 40585, 0]
res = [num for num in a if sum(fact[int(digit)] for digit in str(num)) == num]
print(res)

Output

[145, 2, 40585]

Explanation:

{i: factorial(i) for i in range(10)} iterates over digits 0-9, calculates their factorial using factorial(i) and stores them as key-value pairs. List comprehension filters Strong numbers by iterating over each number’s digits, fetching their precomputed factorials, summing them and checking if the sum equals the original number if true, it’s included in res.

Using math.factorial()

This method uses Python’s built-in math.factorial() compute factorials directly. It simplifies the code but recalculates factorials every time, making it slightly slower than precomputed factorials.

Python

from math import factorial

a = [145, 375, 100, 2, 10, 40585, 0]
res = [num for num in a if sum(factorial(int(digit)) for digit in str(num)) == num]
print(res)

Output

[145, 2, 40585]

Explanation: List comprehension iterates through each number, extracts its digits, computes their factorials using math.factorial(int(digit)), sums them and includes the number in res if the sum matches the original number.

Using iterative factorial calculation

Here, we define a function to calculate factorials using a loop. This method avoids using external libraries but is slower because it recalculates factorials repeatedly.

Python

def factorial(n):
    fact = 1
    for i in range(2, n + 1):
        fact *= i
    return fact

def is_strong(n):
    return sum(factorial(int(digit)) for digit in str(n)) == n

a = [145, 375, 100, 2, 10, 40585, 0]
res = [num for num in a if is_strong(num)]
print(res)

Output

[145, 2, 40585]

Explanation: factorial(n) function calculates a number’s factorial iteratively, while is_strong(n) checks if a number is Strong by summing the factorials of its digits. The list comprehension filters Strong numbers from a using is_strong(num), storing the results in res .

Using nested for loop

This method manually computes factorials using a nested loop inside a while loop. It is the most straightforward approach but also the least efficient since it performs redundant calculations.

Python

a = [145, 375, 100, 2, 10, 40585, 0]
res = [] # initializes an empty list 

for num in a:
    if num == 0:
        continue  # 0 is not a strong number

    temp = num
    sum_fact = 0

    while temp > 0:
        digit = temp % 10
        fact = 1

        for i in range(1, digit + 1):  # Manual factorial calculation
            fact *= i
        
        sum_fact += fact
        temp //= 10

    if sum_fact == num:
        res.append(num)

print(res)

Output

[145, 2, 40585]

Explanation: For loop iterates through each number in a, skipping 0. For each number, sum_fact stores the sum of its digits' factorials. Using a while loop, it extracts each digit (temp % 10), calculates its factorial in a for loop (fact *= i), adds it to sum_fact and updates temp (temp //= 10). If sum_fact matches the original number, it is added to res.