83408 has 20 divisors (see below), whose sum is σ = 174468. Its totient is φ = 38400.

The previous prime is 83407. The next prime is 83417. The reversal of 83408 is 80438.

It can be written as a sum of positive squares in 2 ways, for example, as 53824 + 29584 = 232^2 + 172^2 .

It is a plaindrome in base 14.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (83401) by changing a digit.

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, 8 + ... + 408.

2⁸³⁴⁰⁸ 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 83408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87234).

83408 is an abundant number, since it is smaller than the sum of its proper divisors (91060).

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

83408 is a wasteful number, since it uses less digits than its factorization.

83408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 422 (or 416 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 23.

The square root of 83408 is about 288.8044320990. The cubic root of 83408 is about 43.6920648108.

The spelling of 83408 in words is "eighty-three thousand, four hundred eight".