40416 has 24 divisors (see below), whose sum is σ = 106344. Its totient is φ = 13440.

The previous prime is 40387. The next prime is 40423. The reversal of 40416 is 61404.

40416 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (24).

It is a plaindrome in base 7.

It is a zygodrome in base 7.

It is a junction number, because it is equal to n+sod(n) for n = 40395 and 40404.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 115 + ... + 306.

It is an arithmetic number, because the mean of its divisors is an integer number (4431).

2⁴⁰⁴¹⁶ is an apocalyptic number.

It is an amenable number.

40416 is an abundant number, since it is smaller than the sum of its proper divisors (65928).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (53172).

40416 is a wasteful number, since it uses less digits than its factorization.

40416 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 434 (or 426 counting only the distinct ones).

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

The square root of 40416 is about 201.0373099701. The cubic root of 40416 is about 34.3176686220.

Subtracting from 40416 its sum of digits (15), we obtain a square (40401 = 201²).

The spelling of 40416 in words is "forty thousand, four hundred sixteen".