72400 has 30 divisors (see below), whose sum is σ = 174902. Its totient is φ = 28800.

The previous prime is 72383. The next prime is 72421. The reversal of 72400 is 427.

It can be written as a sum of positive squares in 3 ways, for example, as 576 + 71824 = 24^2 + 268^2 .

It is a congruent number.

It is an unprimeable number.

72400 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 5 ways as a sum of consecutive naturals, for example, 310 + ... + 490.

2⁷²⁴⁰⁰ 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 72400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87451).

72400 is an abundant number, since it is smaller than the sum of its proper divisors (102502).

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

72400 is a wasteful number, since it uses less digits than its factorization.

72400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 199 (or 188 counting only the distinct ones).

The product of its (nonzero) digits is 56, while the sum is 13.

The square root of 72400 is about 269.0724809415. The cubic root of 72400 is about 41.6785743744.

Adding to 72400 its reverse (427), we get a palindrome (72827).

The spelling of 72400 in words is "seventy-two thousand, four hundred", and thus it is an iban number.