396072 has 24 divisors (see below), whose sum is σ = 1072890. Its totient is φ = 132000.

The previous prime is 396061. The next prime is 396079. The reversal of 396072 is 270693.

It can be written as a sum of positive squares in only one way, i.e., 224676 + 171396 = 474^2 + 414^2 .

It is a tau number, because it is divible by the number of its divisors (24).

It is not an unprimeable number, because it can be changed into a prime (396079) by changing a digit.

396072 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 2679 + ... + 2822.

2³⁹⁶⁰⁷² is an apocalyptic number.

It is an amenable number.

396072 is an abundant number, since it is smaller than the sum of its proper divisors (676818).

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

396072 is a wasteful number, since it uses less digits than its factorization.

396072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5513 (or 5506 counting only the distinct ones).

The product of its (nonzero) digits is 2268, while the sum is 27.

The square root of 396072 is about 629.3425140573. The cubic root of 396072 is about 73.4386549087.

The spelling of 396072 in words is "three hundred ninety-six thousand, seventy-two".