393648 has 40 divisors (see below), whose sum is σ = 1041600. Its totient is φ = 128064.

The previous prime is 393637. The next prime is 393649. The reversal of 393648 is 846393.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 393648.

It is not an unprimeable number, because it can be changed into a prime (393649) by changing a digit.

393648 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 7 ways as a sum of consecutive naturals, for example, 2763 + ... + 2901.

It is an arithmetic number, because the mean of its divisors is an integer number (26040).

393648 is a Friedman number, since it can be written as 4*((9+6)*3^8-3), using all its digits and the basic arithmetic operations.

2³⁹³⁶⁴⁸ 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 393648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (520800).

393648 is an abundant number, since it is smaller than the sum of its proper divisors (647952).

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

393648 is a wasteful number, since it uses less digits than its factorization.

393648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 209 (or 203 counting only the distinct ones).

The product of its digits is 15552, while the sum is 33.

The square root of 393648 is about 627.4137390909. The cubic root of 393648 is about 73.2885309443.

The spelling of 393648 in words is "three hundred ninety-three thousand, six hundred forty-eight".