45972 has 18 divisors (see below), whose sum is σ = 116298. Its totient is φ = 15312.

The previous prime is 45971. The next prime is 45979. The reversal of 45972 is 27954.

45972 is nontrivially palindromic in base 5.

45972 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 41616 + 4356 = 204^2 + 66^2 .

It is a tau number, because it is divible by the number of its divisors (18).

It is a super-2 number, since 2×45972² = 4226849568, which contains 22 as substring.

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

It is an Ulam number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (45971) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 603 + ... + 674.

It is an arithmetic number, because the mean of its divisors is an integer number (6461).

2⁴⁵⁹⁷² is an apocalyptic number.

It is an amenable number.

45972 is an abundant number, since it is smaller than the sum of its proper divisors (70326).

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

45972 is a wasteful number, since it uses less digits than its factorization.

45972 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1287 (or 1282 counting only the distinct ones).

The product of its digits is 2520, while the sum is 27.

The square root of 45972 is about 214.4108206225. The cubic root of 45972 is about 35.8232072824.

The spelling of 45972 in words is "forty-five thousand, nine hundred seventy-two".