Number decoder
Enter any whole number up to 15 digits. You get more than 25 exact properties, computed in your browser.
What the properties mean
Prime factorisation writes the number as a product of primes; every whole number above 1 has exactly one. σ(n) is the sum of all divisors, and comparing σ(n) − n with n tells you whether a number is perfect (equal), abundant (greater) or deficient (less). φ(n), Euler's totient, counts the numbers below n that share no factor with it and is central to RSA encryption.
A Harshad number is divisible by the sum of its digits. The digital root is what you get by summing digits until one remains; it equals the remainder after dividing by 9. Base conversions show the same quantity written in binary, octal, hexadecimal and base 36.
Read more in primes and encryption and number bases.
Frequently asked questions
How large a number can I decode?
Up to 15 digits. That keeps every result exact in standard browser arithmetic.
Is my number stored?
No. All calculations happen in your browser.
What is a semiprime?
A number that is the product of exactly two primes, such as 36118 = 2 × 18,059.