10406400 has 120 divisors (see below), whose sum is σ = 34503744. Its totient is φ = 2764800.

The previous prime is 10406393. The next prime is 10406423. The reversal of 10406400 is 460401.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 10406400.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 38265 + ... + 38535.

Almost surely, 2^10406400 is an apocalyptic number.

10406400 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 10406400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17251872).

10406400 is an abundant number, since it is smaller than the sum of its proper divisors (24097344).

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

10406400 is an equidigital number, since it uses as much as digits as its factorization.

10406400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 302 (or 281 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 10406400 is about 3225.8952245850. The cubic root of 10406400 is about 218.3233425234.

Adding to 10406400 its reverse (460401), we get a palindrome (10866801).

The spelling of 10406400 in words is "ten million, four hundred six thousand, four hundred".