961584 has 80 divisors (see below), whose sum is σ = 2833152. Its totient is φ = 278784.

The previous prime is 961567. The next prime is 961601. The reversal of 961584 is 485169.

It is an interprime number because it is at equal distance from previous prime (961567) and next prime (961601).

It is a Smith number, since the sum of its digits (33) coincides with the sum of the digits of its prime factors.

Its product of digits (8640) is a multiple of the sum of its prime divisors (108).

961584 is a modest number, since divided by 1584 gives 96 as remainder.

It is a zygodrome in base 7.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 961584.

It is an unprimeable number.

961584 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 14319 + ... + 14385.

2⁹⁶¹⁵⁸⁴ 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 961584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1416576).

961584 is an abundant number, since it is smaller than the sum of its proper divisors (1871568).

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

961584 is a wasteful number, since it uses less digits than its factorization.

961584 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 114 (or 108 counting only the distinct ones).

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

The square root of 961584 is about 980.6038955664. The cubic root of 961584 is about 98.7027098250.

The spelling of 961584 in words is "nine hundred sixty-one thousand, five hundred eighty-four".