9785916000 has 288 divisors, whose sum is σ = 39692697408. Its totient is φ = 2236723200.

The previous prime is 9785915999. The next prime is 9785916011. The reversal of 9785916000 is 6195879.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

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, 232584 + ... + 271416.

It is an arithmetic number, because the mean of its divisors is an integer number (137821866).

Almost surely, 2^9785916000 is an apocalyptic number.

9785916000 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 9785916000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (19846348704).

9785916000 is an abundant number, since it is smaller than the sum of its proper divisors (29906781408).

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

9785916000 is a wasteful number, since it uses less digits than its factorization.

9785916000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 38871 (or 38850 counting only the distinct ones).

The product of its (nonzero) digits is 136080, while the sum is 45.

The square root of 9785916000 is about 98923.7888477792. The cubic root of 9785916000 is about 2138.9493197321.

The spelling of 9785916000 in words is "nine billion, seven hundred eighty-five million, nine hundred sixteen thousand".