396144 has 80 divisors (see below), whose sum is σ = 1309440. Its totient is φ = 112320.

The previous prime is 396119. The next prime is 396157. The reversal of 396144 is 441693.

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

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 396144.

It is an unprimeable number.

396144 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2959 + ... + 3089.

It is an arithmetic number, because the mean of its divisors is an integer number (16368).

2³⁹⁶¹⁴⁴ 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 396144, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (654720).

396144 is an abundant number, since it is smaller than the sum of its proper divisors (913296).

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

396144 is a wasteful number, since it uses less digits than its factorization.

396144 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 155 (or 143 counting only the distinct ones).

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

The square root of 396144 is about 629.3997140133. The cubic root of 396144 is about 73.4431046575.

It can be divided in two parts, 3961 and 44, that added together give a triangular number (4005 = T₈₉).

The spelling of 396144 in words is "three hundred ninety-six thousand, one hundred forty-four".