3972 has 12 divisors (see below), whose sum is σ = 9296. Its totient is φ = 1320.

The previous prime is 3967. The next prime is 3989. The reversal of 3972 is 2793.

3972 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (12).

It is a plaindrome in base 15.

It is a nialpdrome in base 16.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 3972.

It is an unprimeable number.

3972 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, 154 + ... + 177.

3972 is a Friedman number, since it can be written as (9*7)^2+3, using all its digits and the basic arithmetic operations.

It is an amenable number.

3972 is an abundant number, since it is smaller than the sum of its proper divisors (5324).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4648).

3972 is a wasteful number, since it uses less digits than its factorization.

3972 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 338 (or 336 counting only the distinct ones).

The product of its digits is 378, while the sum is 21.

The square root of 3972 is about 63.0238050264. The cubic root of 3972 is about 15.8368843990.

Adding to 3972 its sum of digits (21), we get a palindrome (3993).

It can be divided in two parts, 39 and 72, that added together give a palindrome (111).

The spelling of 3972 in words is "three thousand, nine hundred seventy-two".