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Python Program to Check a Strong Number

Beginner · Numbers

A strong number is a number equal to the sum of the factorials of its digits, where the factorial of n, written n!, is 1 x 2 x 3 up to n. 145 is a strong number because 1! + 4! + 5! = 1 + 24 + 120 = 145.

Program

strong_number.py
num = 145 # or: num = int(input("Enter a number: "))
total = 0
temp = num # work on a copy so num stays unchanged
while temp > 0:
digit = temp % 10
# Work out the factorial of this digit
fact = 1
for i in range(1, digit + 1):
fact *= i
total += fact
temp //= 10
print(f"Sum of the factorials of the digits of {num}: {total}")
if total == num:
print(num, "is a strong number")
else:
print(num, "is not a strong number")
Output
Sum of the factorials of the digits of 145: 145
145 is a strong number

How it works

  1. temp % 10 takes the last digit and temp //= 10 drops it, so the while loop visits every digit.
  2. The inner for loop works out the factorial of the digit by multiplying 1 x 2 x ... up to the digit.
  3. For the digit 0 the inner loop does not run and fact stays 1, which is right, because 0! is 1.
  4. If the factorials add up to the number itself, it is a strong number.

Another way to write it

Using math.factorial()

Using math.factorial()
import math
def is_strong(n):
return n == sum(math.factorial(int(d)) for d in str(n))
print("Strong numbers up to 50000:")
print([n for n in range(1, 50001) if is_strong(n)])
Output
Strong numbers up to 50000:
[1, 2, 145, 40585]

math.factorial() replaces the inner loop. Only four strong numbers exist in all: 1, 2, 145 and 40585.

Try it yourself

Speed up the check by working out the factorials of 0 to 9 once, into a list, and looking each digit up.

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