33972 has 24 divisors (see below), whose sum is σ = 84000. Its totient is φ = 10656.

The previous prime is 33967. The next prime is 33997. The reversal of 33972 is 27933.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 154 + ... + 302.

It is an arithmetic number, because the mean of its divisors is an integer number (3500).

2³³⁹⁷² 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 33972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (42000).

33972 is an abundant number, since it is smaller than the sum of its proper divisors (50028).

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

33972 is a wasteful number, since it uses less digits than its factorization.

33972 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 175 (or 173 counting only the distinct ones).

The product of its digits is 1134, while the sum is 24.

The square root of 33972 is about 184.3149478474. The cubic root of 33972 is about 32.3872225184.

The spelling of 33972 in words is "thirty-three thousand, nine hundred seventy-two".