36576 has 36 divisors (see below), whose sum is σ = 104832. Its totient is φ = 12096.

The previous prime is 36571. The next prime is 36583. The reversal of 36576 is 67563.

36576 is a `hidden beast` number, since 3 + 657 + 6 = 666.

It is a tau number, because it is divible by the number of its divisors (36).

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 36576.

It is not an unprimeable number, because it can be changed into a prime (36571) by changing a digit.

36576 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 5 ways as a sum of consecutive naturals, for example, 225 + ... + 351.

It is an arithmetic number, because the mean of its divisors is an integer number (2912).

2³⁶⁵⁷⁶ is an apocalyptic number.

36576 is a gapful number since it is divisible by the number (36) formed by its first and last digit.

36576 is the 96-th decagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 36576, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (52416).

36576 is an abundant number, since it is smaller than the sum of its proper divisors (68256).

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

36576 is a wasteful number, since it uses less digits than its factorization.

36576 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 143 (or 132 counting only the distinct ones).

The product of its digits is 3780, while the sum is 27.

The square root of 36576 is about 191.2485294061. The cubic root of 36576 is about 33.1944443212.

It can be divided in two parts, 3657 and 6, that added together give a palindrome (3663).

The spelling of 36576 in words is "thirty-six thousand, five hundred seventy-six".