Number Properties Calculator
Enter a number to instantly fill the properties below. Leave empty to keep values blank.
| Property | Value |
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About the Number Properties Calculator
The Number Properties Calculator is an advanced online tool that reveals detailed mathematical properties of any number. Just enter a number and the calculator instantly generates results across basic arithmetic, divisors, prime factors, special classifications, and numeric representations. You can even download a professional PDF report with all computed values.
This tool is ideal for students, teachers, researchers, and math enthusiasts who want to quickly analyze numbers without manual calculations. It covers everything from prime tests, factorial, digital root, perfect numbers, Fibonacci check to binary, octal, and hexadecimal representations.
Key Properties Computed
Basic Properties
- Absolute Value: |x|
- Sign: Positive, Negative, or Zero
- Digital Root: Repeated digit sum until single digit
- Sum of Digits: Σ (all digits)
- Reciprocal: 1 ÷ x
- Square: x²
- Square Root: √x
- Cube: x³
- Cube Root: ∛x
- Logarithm (log₁₀x): base-10 log
- Natural Log (ln x): log base e
- Exponential (eˣ): exponential function
Integer & Divisors
- Even / Odd: x mod 2
- Prime Test: Checks divisibility (Prime = Yes/No)
- Smallest Prime Factor: First divisor ≥ 2
- Greatest Proper Divisor: Largest divisor less than n
- Divisor Count: Number of divisors of n
- Factorial: n! = 1 × 2 × … × n (valid for n ≤ 20)
- Trailing Zeros in n!: Count of factors of 5 in factorial expansion
- Number Classification: Perfect / Abundant / Deficient (based on sum of proper divisors)
Special Numbers
- Palindrome: Same digits forward & backward
- Armstrong Number: Σ(dᵏ) = n, where k = number of digits
- Harshad (Niven) Number: n mod (sum of digits) = 0
- Perfect Number: Sum of divisors (excluding n) = n
- Fibonacci Test: 5n² ± 4 is a perfect square
- Happy Number: Repeated sum of squares of digits leads to 1
- Triangular Number: n = k(k+1)/2 for some k
- Square-free Number: Not divisible by any perfect square > 1
- Automorphic Number: n² ends with digits of n
- Kaprekar Number: Split square of n, sum of parts = n
- Multiplicative Persistence: Steps needed until digit product is single digit
- Collatz Steps: Iterations until sequence reaches 1 (3n+1 problem)
Representations
- Binary: Base-2 representation
- Octal: Base-8 representation
- Hexadecimal: Base-16 representation
- Nearest Prime: Closest prime to n
How to Use the Number Properties Calculator
- Enter any integer or decimal number in the input box.
- Instantly view all computed properties in categorized sections.
- Download a professional PDF report with full details.
- Click reset to clear the input and start fresh.