83728000 has 64 divisors (see below), whose sum is σ = 208208520. Its totient is φ = 33484800.

The previous prime is 83727997. The next prime is 83728049. The reversal of 83728000 is 82738.

83728000 = T₄₅ + T₄₆ + ... + T₇₉₄.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 48776256 + 34951744 = 6984^2 + 5912^2 .

It is a tau number, because it is divible by the number of its divisors (64).

It is a self number, because there is not a number n which added to its sum of digits gives 83728000.

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 7 ways as a sum of consecutive naturals, for example, 13384 + ... + 18616.

Almost surely, 2^83728000 is an apocalyptic number.

83728000 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 83728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (104104260).

83728000 is an abundant number, since it is smaller than the sum of its proper divisors (124480520).

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

83728000 is an equidigital number, since it uses as much as digits as its factorization.

83728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5262 (or 5240 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 28.

The square root of 83728000 is about 9150.3005415123. The cubic root of 83728000 is about 437.4786928399.

The spelling of 83728000 in words is "eighty-three million, seven hundred twenty-eight thousand".