393638400 has 480 divisors, whose sum is σ = 1552668480. Its totient is φ = 97320960.

The previous prime is 393638393. The next prime is 393638423. The reversal of 393638400 is 4836393.

393638400 = 56³ + 57³ + ... + 199³.

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 5875167 + ... + 5875233.

It is an arithmetic number, because the mean of its divisors is an integer number (3234726).

Almost surely, 2^393638400 is an apocalyptic number.

393638400 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 393638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (776334240).

393638400 is an abundant number, since it is smaller than the sum of its proper divisors (1159030080).

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

393638400 is a wasteful number, since it uses less digits than its factorization.

393638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 121 (or 94 counting only the distinct ones).

The product of its (nonzero) digits is 46656, while the sum is 36.

The square root of 393638400 is about 19840.3225780228. The cubic root of 393638400 is about 732.8793517040.

It can be divided in two parts, 393 and 638400, that multiplied together give a triangular number (250891200 = T₂₂₄₀₀).

The spelling of 393638400 in words is "three hundred ninety-three million, six hundred thirty-eight thousand, four hundred".