89408 has 28 divisors (see below), whose sum is σ = 195072. Its totient is φ = 40320.

The previous prime is 89399. The next prime is 89413. The reversal of 89408 is 80498.

89408 is an admirable number.

It is a congruent number.

It is an unprimeable number.

89408 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, 641 + ... + 767.

2⁸⁹⁴⁰⁸ is an apocalyptic number.

89408 is a gapful number since it is divisible by the number (88) 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 89408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (97536).

89408 is an abundant number, since it is smaller than the sum of its proper divisors (105664).

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

89408 is a wasteful number, since it uses less digits than its factorization.

89408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 150 (or 140 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 29.

The square root of 89408 is about 299.0117054565. The cubic root of 89408 is about 44.7155722844.

The spelling of 89408 in words is "eighty-nine thousand, four hundred eight".