82756800 has 252 divisors, whose sum is σ = 336566256. Its totient is φ = 18892800.

The previous prime is 82756787. The next prime is 82756853. The reversal of 82756800 is 865728.

It is a tau number, because it is divible by the number of its divisors (252).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 100390 + ... + 101210.

Almost surely, 2^82756800 is an apocalyptic number.

82756800 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 82756800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (168283128).

82756800 is an abundant number, since it is smaller than the sum of its proper divisors (253809456).

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

82756800 is a wasteful number, since it uses less digits than its factorization.

82756800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 856 (or 838 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 36.

The square root of 82756800 is about 9097.0764534547. The cubic root of 82756800 is about 435.7806039237.

The spelling of 82756800 in words is "eighty-two million, seven hundred fifty-six thousand, eight hundred".