82993200 has 240 divisors, whose sum is σ = 289314816. Its totient is φ = 20275200.

The previous prime is 82993199. The next prime is 82993217. The reversal of 82993200 is 239928.

It is a tau number, because it is divible by the number of its divisors (240).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 855552 + ... + 855648.

Almost surely, 2^82993200 is an apocalyptic number.

82993200 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 82993200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (144657408).

82993200 is an abundant number, since it is smaller than the sum of its proper divisors (206321616).

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

82993200 is a wasteful number, since it uses less digits than its factorization.

82993200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 172 (or 161 counting only the distinct ones).

The product of its (nonzero) digits is 7776, while the sum is 33.

The square root of 82993200 is about 9110.0603730162. The cubic root of 82993200 is about 436.1951543380.

The spelling of 82993200 in words is "eighty-two million, nine hundred ninety-three thousand, two hundred".