82972032 has 128 divisors (see below), whose sum is σ = 259096320. Its totient is φ = 23193600.

The previous prime is 82972013. The next prime is 82972037. The reversal of 82972032 is 23027928.

It is a tau number, because it is divible by the number of its divisors (128).

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a junction number, because it is equal to n+sod(n) for n = 82971984 and 82972002.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82972037) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 54157 + ... + 55667.

It is an arithmetic number, because the mean of its divisors is an integer number (2024190).

Almost surely, 2^82972032 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 82972032, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129548160).

82972032 is an abundant number, since it is smaller than the sum of its proper divisors (176124288).

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

82972032 is a wasteful number, since it uses less digits than its factorization.

82972032 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1552 (or 1540 counting only the distinct ones).

The product of its (nonzero) digits is 12096, while the sum is 33.

The square root of 82972032 is about 9108.8985064057. The cubic root of 82972032 is about 436.1580663029.

The spelling of 82972032 in words is "eighty-two million, nine hundred seventy-two thousand, thirty-two".