90400 has 36 divisors (see below), whose sum is σ = 222642. Its totient is φ = 35840.

The previous prime is 90397. The next prime is 90401. The reversal of 90400 is 409.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 38416 + 51984 = 196^2 + 228^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (90401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 744 + ... + 856.

2⁹⁰⁴⁰⁰ 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 90400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (111321).

90400 is an abundant number, since it is smaller than the sum of its proper divisors (132242).

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

90400 is a wasteful number, since it uses less digits than its factorization.

90400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 133 (or 120 counting only the distinct ones).

The product of its (nonzero) digits is 36, while the sum is 13.

The square root of 90400 is about 300.6659275675. The cubic root of 90400 is about 44.8803405318.

Adding to 90400 its reverse (409), we get a palindrome (90809).

The spelling of 90400 in words is "ninety thousand, four hundred".