396864 has 84 divisors (see below), whose sum is σ = 1248156. Its totient is φ = 119808.

The previous prime is 396833. The next prime is 396871. The reversal of 396864 is 468693.

396864 = 4³ + 5³ + ... + 35³.

It can be written as a sum of positive squares in 2 ways, for example, as 166464 + 230400 = 408^2 + 480^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 7462 + ... + 7514.

It is an arithmetic number, because the mean of its divisors is an integer number (14859).

396864 is a Friedman number, since it can be written as 96*(38+4^6), using all its digits and the basic arithmetic operations.

2³⁹⁶⁸⁶⁴ 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 396864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (624078).

396864 is an abundant number, since it is smaller than the sum of its proper divisors (851292).

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

396864 is a wasteful number, since it uses less digits than its factorization.

396864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 84 (or 71 counting only the distinct ones).

The product of its digits is 31104, while the sum is 36.

The square root of 396864 is about 629.9714279235. The cubic root of 396864 is about 73.4875725205.

Adding to 396864 its sum of digits (36), we get a square (396900 = 630²).

It can be divided in two parts, 39 and 6864, that added together give a triangular number (6903 = T₁₁₇).

The spelling of 396864 in words is "three hundred ninety-six thousand, eight hundred sixty-four".