83664000 has 384 divisors, whose sum is σ = 347518080. Its totient is φ = 18892800.

The previous prime is 83663981. The next prime is 83664013. The reversal of 83664000 is 46638.

83664000 = 40³ + 41³ + ... + 135³.

It is a tau number, because it is divible by the number of its divisors (384).

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1007959 + ... + 1008041.

It is an arithmetic number, because the mean of its divisors is an integer number (904995).

Almost surely, 2^83664000 is an apocalyptic number.

83664000 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 83664000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (173759040).

83664000 is an abundant number, since it is smaller than the sum of its proper divisors (263854080).

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

83664000 is a wasteful number, since it uses less digits than its factorization.

83664000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 125 (or 100 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 27.

The square root of 83664000 is about 9146.8027200766. The cubic root of 83664000 is about 437.3671977875.

The spelling of 83664000 in words is "eighty-three million, six hundred sixty-four thousand".