10400 has 36 divisors (see below), whose sum is σ = 27342. Its totient is φ = 3840.

The previous prime is 10399. The next prime is 10427. The reversal of 10400 is 401.

It can be written as a sum of positive squares in 3 ways, for example, as 5776 + 4624 = 76^2 + 68^2 .

It is a Harshad number since it is a multiple of its sum of digits (5).

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

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 794 + ... + 806.

2¹⁰⁴⁰⁰ is an apocalyptic number.

10400 is a gapful number since it is divisible by the number (10) 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 10400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (13671).

10400 is an abundant number, since it is smaller than the sum of its proper divisors (16942).

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

10400 is a wasteful number, since it uses less digits than its factorization.

10400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 33 (or 20 counting only the distinct ones).

The product of its (nonzero) digits is 4, while the sum is 5.

The square root of 10400 is about 101.9803902719. The cubic root of 10400 is about 21.8278576612.

Adding to 10400 its reverse (401), we get a palindrome (10801).

Subtracting from 10400 its reverse (401), we obtain a palindrome (9999).

The spelling of 10400 in words is "ten thousand, four hundred", and thus it is an iban number.