Calculators
Strong Number Calculator
Check whether an integer equals the sum of its digit factorials with exact strong number arithmetic, privately in your browser.
A strong number equals the sum of its digit factorials. For example, 145 = 1! + 4! + 5! = 1 + 24 + 120. Remember that 0! = 1, so zero does not qualify. Enter up to 1000 digits; leading zeros are removed. Calculations stay in your browser.
How to check a strong number
A strong number (also called a factorion) is a nonnegative base-10 integer equal to the sum of the factorials of its digits. For 145, 1! + 4! + 5! = 1 + 24 + 120 = 145, so it qualifies. For 123, the sum is 1 + 2 + 6 = 9, so it does not. Other examples are 1, 2 and 40585. By definition 0! = 1, so zero does not qualify and each zero digit contributes one. Enter 1 to 1000 decimal digits without signs, separators, decimals or exponent notation. Surrounding whitespace is accepted and leading zeros are removed before calculation: 00145 is checked as 145. Each digit factorial and the total use exact BigInt arithmetic. This checks one integer and shows the factorial expression; it does not search a range. Unlike an Armstrong number, this uses factorials rather than powers. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is a strong number?
A strong number equals the sum of the factorials of its decimal digits. For example, 145 = 1! + 4! + 5!. It is also called a factorion.
Is zero a strong number?
No. The factorial of zero is one, so the digit factorial sum of 0 is 1. Every zero digit contributes 1 to the sum.
How are leading zeros handled?
Leading zeros are removed before calculating. For example, 00145 is treated as 145, so the extra zeros do not contribute to its sum.
Is this the same as an Armstrong number?
No. Strong numbers sum digit factorials; Armstrong numbers sum each digit raised to the number of digits.
Are large integers exact and private?
Yes. Up to 1000 input digits are processed with exact BigInt arithmetic entirely in your browser.