81972 has 60 divisors (see below), whose sum is σ = 243936. Its totient is φ = 23760.

The previous prime is 81971. The next prime is 81973. The reversal of 81972 is 27918.

It is an interprime number because it is at equal distance from previous prime (81971) and next prime (81973).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (81971) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 3553 + ... + 3575.

2⁸¹⁹⁷² 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 81972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (121968).

81972 is an abundant number, since it is smaller than the sum of its proper divisors (161964).

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

81972 is a wasteful number, since it uses less digits than its factorization.

81972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 50 (or 39 counting only the distinct ones).

The product of its digits is 1008, while the sum is 27.

The square root of 81972 is about 286.3075269706. The cubic root of 81972 is about 43.4398693565.

The spelling of 81972 in words is "eighty-one thousand, nine hundred seventy-two".