82534800 has 120 divisors (see below), whose sum is σ = 267234880. Its totient is φ = 21772800.

The previous prime is 82534799. The next prime is 82534807. The reversal of 82534800 is 843528.

It is a tau number, because it is divible by the number of its divisors (120).

It is a super-2 number, since 2×82534800² = 13623986422080000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (30) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is not an unprimeable number, because it can be changed into a prime (82534807) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 130485 + ... + 131115.

Almost surely, 2^82534800 is an apocalyptic number.

82534800 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82534800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (133617440).

82534800 is an abundant number, since it is smaller than the sum of its proper divisors (184700080).

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

82534800 is a wasteful number, since it uses less digits than its factorization.

82534800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 761 (or 750 counting only the distinct ones).

The product of its (nonzero) digits is 7680, while the sum is 30.

The square root of 82534800 is about 9084.8665372695. The cubic root of 82534800 is about 435.3905859040.

The spelling of 82534800 in words is "eighty-two million, five hundred thirty-four thousand, eight hundred".