9785664000 has 640 divisors, whose sum is σ = 41365209600. Its totient is φ = 2233958400.

The previous prime is 9785663933. The next prime is 9785664001. The reversal of 9785664000 is 4665879.

It is a tau number, because it is divible by the number of its divisors (640).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (9785664001) 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 63 ways as a sum of consecutive naturals, for example, 12095596 + ... + 12096404.

It is an arithmetic number, because the mean of its divisors is an integer number (64633140).

Almost surely, 2^9785664000 is an apocalyptic number.

9785664000 is a gapful number since it is divisible by the number (90) 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 9785664000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20682604800).

9785664000 is an abundant number, since it is smaller than the sum of its proper divisors (31579545600).

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

9785664000 is an equidigital number, since it uses as much as digits as its factorization.

9785664000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 858 (or 826 counting only the distinct ones).

The product of its (nonzero) digits is 362880, while the sum is 45.

The square root of 9785664000 is about 98922.5151317939. The cubic root of 9785664000 is about 2138.9309593369.

The spelling of 9785664000 in words is "nine billion, seven hundred eighty-five million, six hundred sixty-four thousand".