961584000 has 512 divisors, whose sum is σ = 3635573760. Its totient is φ = 223027200.

The previous prime is 961583993. The next prime is 961584079. The reversal of 961584000 is 485169.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 14351967 + ... + 14352033.

It is an arithmetic number, because the mean of its divisors is an integer number (7100730).

Almost surely, 2^961584000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 961584000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1817786880).

961584000 is an abundant number, since it is smaller than the sum of its proper divisors (2673989760).

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

961584000 is a wasteful number, since it uses less digits than its factorization.

961584000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 135 (or 113 counting only the distinct ones).

The product of its (nonzero) digits is 8640, while the sum is 33.

The square root of 961584000 is about 31009.4179242371. The cubic root of 961584000 is about 987.0270982501.

The spelling of 961584000 in words is "nine hundred sixty-one million, five hundred eighty-four thousand".