83564800 has 108 divisors (see below), whose sum is σ = 225829296. Its totient is φ = 30361600.

The previous prime is 83564777. The next prime is 83564807. The reversal of 83564800 is 846538.

It is not an unprimeable number, because it can be changed into a prime (83564807) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 69807 + ... + 70993.

It is an arithmetic number, because the mean of its divisors is an integer number (2091012).

Almost surely, 2^83564800 is an apocalyptic number.

83564800 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 83564800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (112914648).

83564800 is an abundant number, since it is smaller than the sum of its proper divisors (142264496).

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

83564800 is a wasteful number, since it uses less digits than its factorization.

83564800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1224 (or 1205 counting only the distinct ones).

The product of its (nonzero) digits is 23040, while the sum is 34.

The square root of 83564800 is about 9141.3784518529. The cubic root of 83564800 is about 437.1942680321.

The spelling of 83564800 in words is "eighty-three million, five hundred sixty-four thousand, eight hundred".