208416 has 48 divisors (see below), whose sum is σ = 592704. Its totient is φ = 63744.

The previous prime is 208409. The next prime is 208433. The reversal of 208416 is 614802.

It is a tau number, because it is divible by the number of its divisors (48).

It is a junction number, because it is equal to n+sod(n) for n = 208392 and 208401.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1165 + ... + 1331.

It is an arithmetic number, because the mean of its divisors is an integer number (12348).

2²⁰⁸⁴¹⁶ is an apocalyptic number.

208416 is a gapful number since it is divisible by the number (26) 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 208416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (296352).

208416 is an abundant number, since it is smaller than the sum of its proper divisors (384288).

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

208416 is a wasteful number, since it uses less digits than its factorization.

208416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 193 (or 185 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 21.

The square root of 208416 is about 456.5260124024. The cubic root of 208416 is about 59.2893950116.

The spelling of 208416 in words is "two hundred eight thousand, four hundred sixteen".