85408 has 24 divisors (see below), whose sum is σ = 179172. Its totient is φ = 39936.

The previous prime is 85381. The next prime is 85411. The reversal of 85408 is 80458.

85408 is nontrivially palindromic in base 12.

It can be written as a sum of positive squares in 2 ways, for example, as 85264 + 144 = 292^2 + 12^2 .

It is an unprimeable number.

85408 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 3 ways as a sum of consecutive naturals, for example, 466 + ... + 622.

2⁸⁵⁴⁰⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 85408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (89586).

85408 is an abundant number, since it is smaller than the sum of its proper divisors (93764).

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

85408 is a wasteful number, since it uses less digits than its factorization.

85408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 184 (or 176 counting only the distinct ones).

The product of its (nonzero) digits is 1280, while the sum is 25.

The square root of 85408 is about 292.2464713217. The cubic root of 85408 is about 44.0385337367.

Subtracting from 85408 its reverse (80458), we obtain a triangular number (4950 = T₉₉).

It can be divided in two parts, 8 and 5408, that multiplied together give a square (43264 = 208²).

The spelling of 85408 in words is "eighty-five thousand, four hundred eight".