363648 has 32 divisors (see below), whose sum is σ = 966960. Its totient is φ = 121088.

The previous prime is 363619. The next prime is 363659. The reversal of 363648 is 846363.

363648 is nontrivially palindromic in base 13.

It is a tau number, because it is divible by the number of its divisors (32).

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

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 363648.

It is an unprimeable number.

363648 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 3 ways as a sum of consecutive naturals, for example, 90 + ... + 857.

2³⁶³⁶⁴⁸ 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 363648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (483480).

363648 is an abundant number, since it is smaller than the sum of its proper divisors (603312).

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

363648 is an equidigital number, since it uses as much as digits as its factorization.

363648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 964 (or 952 counting only the distinct ones).

The product of its digits is 10368, while the sum is 30.

The square root of 363648 is about 603.0323374414. The cubic root of 363648 is about 71.3773468925.

It can be divided in two parts, 36 and 3648, that multiplied together give a triangular number (131328 = T₅₁₂).

The spelling of 363648 in words is "three hundred sixty-three thousand, six hundred forty-eight".