38624400 has 90 divisors (see below), whose sum is σ = 134049890. Its totient is φ = 10298880.

The previous prime is 38624389. The next prime is 38624413. The reversal of 38624400 is 442683.

38624400 is a `hidden beast` number, since 38 + 624 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 5308416 + 33315984 = 2304^2 + 5772^2 .

It is a tau number, because it is divible by the number of its divisors (90).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1765 + ... + 8964.

Almost surely, 2^38624400 is an apocalyptic number.

38624400 is a gapful number since it is divisible by the number (30) 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 38624400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (67024945).

38624400 is an abundant number, since it is smaller than the sum of its proper divisors (95425490).

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

38624400 is a wasteful number, since it uses less digits than its factorization.

38624400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10753 (or 10739 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

The square root of 38624400 is about 6214.8531760614. The cubic root of 38624400 is about 338.0289647575.

The spelling of 38624400 in words is "thirty-eight million, six hundred twenty-four thousand, four hundred".