A strong number is a number where the sum of the factorial of its individual digits is equal to the number itself.
Understanding Strong Numbers
According to the provided reference, a number is considered a strong number if the sum of the factorial of its digits equals the original number. Let's break this down:
- Factorial: The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 4! = 4 3 2 * 1 = 24.
- Digit Factorial Sum: Calculate the factorial of each digit in the number and add these factorials together.
- Strong Number Check: If the sum of the digit factorials equals the original number, then it's a strong number.
Example
The reference provides the example of 145. Let's verify:
- 1! = 1
- 4! = 4 3 2 * 1 = 24
- 5! = 5 4 3 2 1 = 120
Therefore, 1! + 4! + 5! = 1 + 24 + 120 = 145. Since the sum equals the original number (145), it is indeed a strong number.
Practical Insights
- Strong numbers are relatively rare.
- Calculating factorials is essential for identifying strong numbers.
- This concept provides a practical application of the factorial function.
