83760 has 40 divisors (see below), whose sum is σ = 260400. Its totient is φ = 22272.

The previous prime is 83737. The next prime is 83761. The reversal of 83760 is 6738.

It is a tau number, because it is divible by the number of its divisors (40).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a self number, because there is not a number n which added to its sum of digits gives 83760.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 83760.

It is not an unprimeable number, because it can be changed into a prime (83761) by changing a digit.

83760 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 66 + ... + 414.

It is an arithmetic number, because the mean of its divisors is an integer number (6510).

2⁸³⁷⁶⁰ is an apocalyptic number.

83760 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 83760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130200).

83760 is an abundant number, since it is smaller than the sum of its proper divisors (176640).

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

83760 is a wasteful number, since it uses less digits than its factorization.

83760 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 365 (or 359 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 24.

The square root of 83760 is about 289.4131994226. The cubic root of 83760 is about 43.7534419061.

The spelling of 83760 in words is "eighty-three thousand, seven hundred sixty".