82618800 has 180 divisors, whose sum is σ = 291413640. Its totient is φ = 19993600.

The previous prime is 82618799. The next prime is 82618819. The reversal of 82618800 is 881628.

It is a super-2 number, since 2×82618800² = 13651732226880000, which contains 22 as substring.

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 144916 + ... + 145484.

Almost surely, 2^82618800 is an apocalyptic number.

82618800 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 82618800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (145706820).

82618800 is an abundant number, since it is smaller than the sum of its proper divisors (208794840).

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

82618800 is a wasteful number, since it uses less digits than its factorization.

82618800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 612 (or 590 counting only the distinct ones).

The product of its (nonzero) digits is 6144, while the sum is 33.

The square root of 82618800 is about 9089.4884344500. The cubic root of 82618800 is about 435.5382424435.

The spelling of 82618800 in words is "eighty-two million, six hundred eighteen thousand, eight hundred".