363968 has 42 divisors (see below), whose sum is σ = 810768. Its totient is φ = 161920.

The previous prime is 363967. The next prime is 363977. The reversal of 363968 is 869363.

363968 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

Its product of digits (23328) is a multiple of the sum of its prime factors (81).

It is a nialpdrome in base 13.

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 363968.

It is not an unprimeable number, because it can be changed into a prime (363967) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 7721 + ... + 7767.

It is an arithmetic number, because the mean of its divisors is an integer number (19304).

2³⁶³⁹⁶⁸ 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 363968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (405384).

363968 is an abundant number, since it is smaller than the sum of its proper divisors (446800).

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

363968 is a wasteful number, since it uses less digits than its factorization.

363968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 81 (or 60 counting only the distinct ones).

The product of its digits is 23328, while the sum is 35.

The square root of 363968 is about 603.2976048353. The cubic root of 363968 is about 71.3982774394.

It can be divided in two parts, 363 and 968, that added together give a palindrome (1331).

The spelling of 363968 in words is "three hundred sixty-three thousand, nine hundred sixty-eight".