89964000 has 576 divisors, whose sum is σ = 403341120. Its totient is φ = 19353600.

The previous prime is 89963999. The next prime is 89964001. The reversal of 89964000 is 46998.

89964000 is a `hidden beast` number, since 8 + 9 + 9 + 640 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (89963999) and next prime (89964001).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (89964001) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 5291992 + ... + 5292008.

It is an arithmetic number, because the mean of its divisors is an integer number (700245).

Almost surely, 2^89964000 is an apocalyptic number.

89964000 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 89964000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (201670560).

89964000 is an abundant number, since it is smaller than the sum of its proper divisors (313377120).

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

89964000 is a wasteful number, since it uses less digits than its factorization.

89964000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 65 (or 34 counting only the distinct ones).

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

The square root of 89964000 is about 9484.9354241344. The cubic root of 89964000 is about 448.0807146237.

It can be divided in two parts, 8996 and 4000, that added together give a square (12996 = 114²).

The spelling of 89964000 in words is "eighty-nine million, nine hundred sixty-four thousand".