Problem #34 Difficulty: 5%

Digit Factorials

Solution Language: Java
View Solution View on Project Euler

Problem Statement

145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: As 1! = 1 and 2! = 2 are not sums they are not included.

Approach

The solution involves:

  1. Determining an upper bound for the search (7 × 9! = 2,540,160)
  2. For each number, computing the sum of factorials of its digits
  3. Checking if the sum equals the original number
  4. Summing all such numbers (excluding 1 and 2)