416400 has 60 divisors (see below), whose sum is σ = 1337712. Its totient is φ = 110720.

The previous prime is 416399. The next prime is 416401. The reversal of 416400 is 4614.

It is an interprime number because it is at equal distance from previous prime (416399) and next prime (416401).

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 (15).

It is a self number, because there is not a number n which added to its sum of digits gives 416400.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 416400.

It is not an unprimeable number, because it can be changed into a prime (416401) 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, 1027 + ... + 1373.

2⁴¹⁶⁴⁰⁰ is an apocalyptic number.

416400 is a gapful number since it is divisible by the number (40) 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 416400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (668856).

416400 is an abundant number, since it is smaller than the sum of its proper divisors (921312).

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

416400 is a wasteful number, since it uses less digits than its factorization.

416400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 368 (or 357 counting only the distinct ones).

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

The square root of 416400 is about 645.2906321961. The cubic root of 416400 is about 74.6741418253.

It can be divided in two parts, 41 and 6400, that added together give a triangular number (6441 = T₁₁₃).

The spelling of 416400 in words is "four hundred sixteen thousand, four hundred".