89760 has 96 divisors (see below), whose sum is σ = 326592. Its totient is φ = 20480.

The previous prime is 89759. The next prime is 89767. The reversal of 89760 is 6798.

89760 = T₅₅ + T₅₆ + ... + T₈₈.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (96).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 89760.

It is not an unprimeable number, because it can be changed into a prime (89767) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 5272 + ... + 5288.

It is an arithmetic number, because the mean of its divisors is an integer number (3402).

2⁸⁹⁷⁶⁰ is an apocalyptic number.

89760 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 89760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (163296).

89760 is an abundant number, since it is smaller than the sum of its proper divisors (236832).

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

89760 is a wasteful number, since it uses less digits than its factorization.

89760 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 46 (or 38 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 30.

The square root of 89760 is about 299.5997329772. The cubic root of 89760 is about 44.7741772955.

89760 divided by its sum of digits (30) gives a palindrome (2992).

Subtracting from 89760 its product of nonzero digits (3024), we obtain a triangular number (86736 = T₄₁₆).

The spelling of 89760 in words is "eighty-nine thousand, seven hundred sixty".