396144000 has 512 divisors, whose sum is σ = 1680307200. Its totient is φ = 89856000.

The previous prime is 396143981. The next prime is 396144029. The reversal of 396144000 is 441693.

396144000 is a `hidden beast` number, since 3 + 9 + 614 + 40 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 3023935 + ... + 3024065.

It is an arithmetic number, because the mean of its divisors is an integer number (3281850).

Almost surely, 2^396144000 is an apocalyptic number.

396144000 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 396144000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (840153600).

396144000 is an abundant number, since it is smaller than the sum of its proper divisors (1284163200).

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

396144000 is a wasteful number, since it uses less digits than its factorization.

396144000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 176 (or 148 counting only the distinct ones).

The product of its (nonzero) digits is 2592, while the sum is 27.

The square root of 396144000 is about 19903.3665494057. The cubic root of 396144000 is about 734.4310465751.

Adding to 396144000 its reverse (441693), we get a palindrome (396585693).

It can be divided in two parts, 3961 and 44000, that added together give a square (47961 = 219²).

The spelling of 396144000 in words is "three hundred ninety-six million, one hundred forty-four thousand".