89964 has 72 divisors (see below), whose sum is σ = 287280. Its totient is φ = 24192.

The previous prime is 89963. The next prime is 89977. The reversal of 89964 is 46998.

89964 = 4³ + 5³ + ... + 24³.

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

It is not an unprimeable number, because it can be changed into a prime (89963) by changing a digit.

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 23 ways as a sum of consecutive naturals, for example, 5284 + ... + 5300.

It is an arithmetic number, because the mean of its divisors is an integer number (3990).

2⁸⁹⁹⁶⁴ is an apocalyptic number.

89964 is a gapful number since it is divisible by the number (84) 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 89964, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (143640).

89964 is an abundant number, since it is smaller than the sum of its proper divisors (197316).

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

89964 is a wasteful number, since it uses less digits than its factorization.

89964 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 44 (or 29 counting only the distinct ones).

The product of its digits is 15552, while the sum is 36.

The square root of 89964 is about 299.9399939988. The cubic root of 89964 is about 44.8080714624.

Adding to 89964 its sum of digits (36), we get a square (90000 = 300²).

The spelling of 89964 in words is "eighty-nine thousand, nine hundred sixty-four".