396105600 has 384 divisors, whose sum is σ = 1481333760. Its totient is φ = 92928000.

The previous prime is 396105599. The next prime is 396105607. The reversal of 396105600 is 6501693.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (396105607) by changing a digit.

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, 12777585 + ... + 12777615.

It is an arithmetic number, because the mean of its divisors is an integer number (3857640).

Almost surely, 2^396105600 is an apocalyptic number.

396105600 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 396105600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (740666880).

396105600 is an abundant number, since it is smaller than the sum of its proper divisors (1085228160).

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

396105600 is a wasteful number, since it uses less digits than its factorization.

It is an anagram of its base 11 representation: 396105600 = (193656000)₁₁.

396105600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 91 (or 52 counting only the distinct ones).

The product of its (nonzero) digits is 4860, while the sum is 30.

The square root of 396105600 is about 19902.4018651016. The cubic root of 396105600 is about 734.4073152522.

The spelling of 396105600 in words is "three hundred ninety-six million, one hundred five thousand, six hundred".