363168 has 72 divisors (see below), whose sum is σ = 1123668. Its totient is φ = 110592.

The previous prime is 363161. The next prime is 363173. The reversal of 363168 is 861363.

It can be written as a sum of positive squares in 2 ways, for example, as 345744 + 17424 = 588^2 + 132^2 .

It is a tau number, because it is divible by the number of its divisors (72).

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

It is an Ulam number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 363168.

It is not an unprimeable number, because it can be changed into a prime (363161) by changing a digit.

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 11 ways as a sum of consecutive naturals, for example, 3696 + ... + 3792.

2³⁶³¹⁶⁸ 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 363168, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (561834).

363168 is an abundant number, since it is smaller than the sum of its proper divisors (760500).

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

363168 is a wasteful number, since it uses less digits than its factorization.

363168 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 126 (or 115 counting only the distinct ones).

The product of its digits is 2592, while the sum is 27.

The square root of 363168 is about 602.6342174155. The cubic root of 363168 is about 71.3459280369.

The spelling of 363168 in words is "three hundred sixty-three thousand, one hundred sixty-eight".