396960 has 48 divisors (see below), whose sum is σ = 1251936. Its totient is φ = 105728.

The previous prime is 396953. The next prime is 396971. The reversal of 396960 is 69693.

396960 = 206² + 207² + ... + 214².

396960 is nontrivially palindromic in base 9.

396960 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (48).

It is a zygodrome in base 9.

It is an unprimeable 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 7 ways as a sum of consecutive naturals, for example, 67 + ... + 893.

It is an arithmetic number, because the mean of its divisors is an integer number (26082).

2³⁹⁶⁹⁶⁰ is an apocalyptic number.

396960 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 396960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (625968).

396960 is an abundant number, since it is smaller than the sum of its proper divisors (854976).

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

396960 is a wasteful number, since it uses less digits than its factorization.

396960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 845 (or 837 counting only the distinct ones).

The product of its (nonzero) digits is 8748, while the sum is 33.

The square root of 396960 is about 630.0476172481. The cubic root of 396960 is about 73.4934975042.

The spelling of 396960 in words is "three hundred ninety-six thousand, nine hundred sixty".