36072 has 32 divisors (see below), whose sum is σ = 100800. Its totient is φ = 11952.

The previous prime is 36067. The next prime is 36073. The reversal of 36072 is 27063.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a plaindrome in base 13.

It is a nialpdrome in base 9.

It is not an unprimeable number, because it can be changed into a prime (36073) by changing a digit.

36072 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 7 ways as a sum of consecutive naturals, for example, 133 + ... + 299.

It is an arithmetic number, because the mean of its divisors is an integer number (3150).

2³⁶⁰⁷² 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 36072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (50400).

36072 is an abundant number, since it is smaller than the sum of its proper divisors (64728).

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

36072 is a wasteful number, since it uses less digits than its factorization.

36072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 182 (or 172 counting only the distinct ones).

The product of its (nonzero) digits is 252, while the sum is 18.

The square root of 36072 is about 189.9263014961. The cubic root of 36072 is about 33.0412706783.

Subtracting from 36072 its reverse (27063), we obtain a palindrome (9009).

The spelling of 36072 in words is "thirty-six thousand, seventy-two".