20400 has 60 divisors (see below), whose sum is σ = 69192. Its totient is φ = 5120.

The previous prime is 20399. The next prime is 20407. The reversal of 20400 is 402.

20400 = 8² + 9² + ... + 39².

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (6).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

20400 is an undulating number in base 13.

It is a nialpdrome in base 12.

It is a zygodrome in base 7.

It is not an unprimeable number, because it can be changed into a prime (20407) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1192 + ... + 1208.

2²⁰⁴⁰⁰ is an apocalyptic number.

20400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 20400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (34596).

20400 is an abundant number, since it is smaller than the sum of its proper divisors (48792).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

20400 is a wasteful number, since it uses less digits than its factorization.

20400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 38 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 6.

The square root of 20400 is about 142.8285685709. The cubic root of 20400 is about 27.3239441609.

Adding to 20400 its reverse (402), we get a palindrome (20802).

It can be divided in two parts, 20 and 400, that multiplied together give a cube (8000 = 20³).

The spelling of 20400 in words is "twenty thousand, four hundred", and thus it is an iban number.