Type any whole number up to one quadrillion and see everything about it at once: prime or composite, even or odd, its prime factorization and divisors, and whether it is a perfect number, a perfect square or cube, triangular, Fibonacci, a palindrome and more.
Last updated:
Any whole number from 0 to 1,000,000,000,000,000 (10^15). Commas and spaces are ignored.
Enter your values to see the result.
Advertisement
Advertisement
How to use the Number Properties Calculator
Type a whole number, for example 28 or 1729 (commas are fine).
Press Check number, or just keep typing: results update as you go.
Read the summary: prime or composite, even or odd and the property tags.
Scroll the properties table for every yes/no test with the reason.
Copy or download the results for homework or notes.
What the number properties mean
Property
Definition
Examples
Prime
Exactly two divisors: 1 and itself
2, 3, 5, 7, 11, 97
Composite
More than two divisors
4, 6, 9, 12, 100
Perfect
Equals the sum of its proper divisors
6, 28, 496, 8128
Abundant
Proper divisors add up to more than the number
12, 18, 20, 24
Perfect square / cube
k² or k³ for a whole number k
49 = 7², 125 = 5³
Triangular
1 + 2 + … + k = k(k + 1)/2
1, 3, 6, 10, 15, 21
Fibonacci
Each term is the sum of the previous two
1, 2, 3, 5, 8, 13, 21
Palindrome
Reads the same backwards
121, 1331, 12321
Armstrong (narcissistic)
Sum of each digit raised to the number of digits equals the number
153 = 1³ + 5³ + 3³, 9474
Harshad (Niven)
Divisible by its digit sum
18, 21, 111, 1729
Happy
Repeatedly summing the squares of the digits reaches 1
7, 10, 13, 19, 23
Square-free
No prime factor appears twice
10, 30, 105
Semiprime
Product of exactly two primes (possibly equal)
4, 6, 15, 77
How the checks work
The calculator first finds the prime factorization, because most other properties follow from it. If n = p₁a × p₂b × …, then the number of divisors is (a + 1)(b + 1)…, the sum of divisors σ(n) is the product of (1 + p + … + pa) for each prime, and Euler’s totient is φ(n) = n × (1 − 1/p₁)(1 − 1/p₂)…. A number is perfect when σ(n) = 2n, a perfect square when every exponent is even, and square-free when every exponent is 1.
Shape tests use exact integer square roots: n is triangular when 8n + 1 is a perfect square, and a Fibonacci number when 5n² + 4 or 5n² − 4 is a perfect square. Primality of large values and the next/previous prime use the Miller–Rabin test with the first twelve primes as bases, which is proven exact far beyond 1015.
Fun examples to try: 1729 is the smallest number that is a sum of two cubes in two different ways (1³ + 12³ = 9³ + 10³). 8128 is the fourth perfect number. 600,851,475,143 factors into four primes, the largest being 6857.
Frequently asked questions
How do I know if a number is prime?
A prime has exactly two divisors, 1 and itself. To check n, try dividing by every prime up to √n; if none divides evenly, n is prime. 97 is prime because 2, 3, 5 and 7 (the primes up to √97 ≈ 9.8) all leave remainders. For large numbers this tool uses the deterministic Miller–Rabin test.
Is 0 or 1 a prime number?
Neither. 1 has only one divisor and 0 is divisible by every positive whole number, so both are classed as neither prime nor composite. 2 is the smallest prime and the only even prime.
What is a perfect number?
A number equal to the sum of its proper divisors (all divisors except itself). 28 is perfect because 1 + 2 + 4 + 7 + 14 = 28. If the sum is larger the number is abundant (12: 1+2+3+4+6 = 16); if smaller it is deficient. Known perfect numbers are rare: 6, 28, 496, 8128, 33,550,336…
How do you find the number of divisors?
Write the prime factorization, add 1 to each exponent and multiply. 360 = 2³ × 3² × 5, so it has (3+1)(2+1)(1+1) = 24 divisors.
How can I tell if a number is triangular or Fibonacci?
n is triangular (1, 3, 6, 10, 15…) exactly when 8n + 1 is a perfect square. n is a Fibonacci number exactly when 5n² + 4 or 5n² − 4 is a perfect square. Both tests are exact, so the tool does not need to list the sequences.
What are the digit sum and digital root?
The digit sum adds the digits (1729 → 1+7+2+9 = 19). Repeating until one digit remains gives the digital root (19 → 10 → 1). A number is divisible by 3 or 9 exactly when its digit sum is.
How big a number can I check?
Any whole number from 0 up to 10^15 (one quadrillion). All tests are exact; factoring a number up to 10^15 takes well under a second in your browser.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.