961584436800 has 3024 divisors, whose sum is σ = 4402935194112. Its totient is φ = 204241305600.

The previous prime is 961584436763. The next prime is 961584436801. The reversal of 961584436800 is 8634485169.

961584436800 is a `hidden beast` number, since 96 + 1 + 58 + 443 + 68 + 0 + 0 = 666.

961584436800 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (961584436801) by changing a digit.

It is a polite number, since it can be written in 431 ways as a sum of consecutive naturals, for example, 31018852785 + ... + 31018852815.

It is an arithmetic number, because the mean of its divisors is an integer number (1455997088).

Almost surely, 2^961584436800 is an apocalyptic number.

961584436800 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 961584436800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2201467597056).

961584436800 is an abundant number, since it is smaller than the sum of its proper divisors (3441350757312).

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

961584436800 is a wasteful number, since it uses less digits than its factorization.

961584436800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 136 (or 90 counting only the distinct ones).

The product of its (nonzero) digits is 4976640, while the sum is 54.

The spelling of 961584436800 in words is "nine hundred sixty-one billion, five hundred eighty-four million, four hundred thirty-six thousand, eight hundred".