82500 has 60 divisors (see below), whose sum is σ = 262416. Its totient is φ = 20000.

The previous prime is 82499. The next prime is 82507. The reversal of 82500 is 528.

Added to its reverse (528) it gives a triangular number (83028 = T₄₀₇).

It is a tau number, because it is divible by the number of its divisors (60).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 82500.

It is not an unprimeable number, because it can be changed into a prime (82507) 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, 7495 + ... + 7505.

2⁸²⁵⁰⁰ 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 82500, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131208).

82500 is an abundant number, since it is smaller than the sum of its proper divisors (179916).

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

82500 is a wasteful number, since it uses less digits than its factorization.

82500 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 38 (or 21 counting only the distinct ones).

The product of its (nonzero) digits is 80, while the sum is 15.

The square root of 82500 is about 287.2281323269. The cubic root of 82500 is about 43.5329384559.

Adding to 82500 its reverse (528), we get a triangular number (83028 = T₄₀₇).

Multiplying 82500 by its reverse (528), we get a square (43560000 = 6600²).

The spelling of 82500 in words is "eighty-two thousand, five hundred".