82728000 has 224 divisors, whose sum is σ = 304312320. Its totient is φ = 22003200.

The previous prime is 82727999. The next prime is 82728011. The reversal of 82728000 is 82728.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

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 31 ways as a sum of consecutive naturals, for example, 215809 + ... + 216191.

Almost surely, 2^82728000 is an apocalyptic number.

82728000 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 82728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (152156160).

82728000 is an abundant number, since it is smaller than the sum of its proper divisors (221584320).

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

82728000 is a wasteful number, since it uses less digits than its factorization.

82728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 419 (or 393 counting only the distinct ones).

The product of its (nonzero) digits is 1792, while the sum is 27.

The square root of 82728000 is about 9095.4933895859. The cubic root of 82728000 is about 435.7300463963.

82728000 divided by its reverse (82728) gives a cube (1000 = 10³).

The spelling of 82728000 in words is "eighty-two million, seven hundred twenty-eight thousand".