963648000 has 480 divisors, whose sum is σ = 3983316480. Its totient is φ = 219340800.

The previous prime is 963647957. The next prime is 963648019. The reversal of 963648000 is 846369.

963648000 is a `hidden beast` number, since 9 + 6 + 3 + 648 + 0 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (480).

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

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, 4031881 + ... + 4032119.

It is an arithmetic number, because the mean of its divisors is an integer number (8298576).

Almost surely, 2^963648000 is an apocalyptic number.

963648000 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 963648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1991658240).

963648000 is an abundant number, since it is smaller than the sum of its proper divisors (3019668480).

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

963648000 is a wasteful number, since it uses less digits than its factorization.

963648000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 285 (or 256 counting only the distinct ones).

The product of its (nonzero) digits is 31104, while the sum is 36.

The square root of 963648000 is about 31042.6802966496. The cubic root of 963648000 is about 987.7327977560.

The spelling of 963648000 in words is "nine hundred sixty-three million, six hundred forty-eight thousand".