961264800 has 288 divisors, whose sum is σ = 3509775360. Its totient is φ = 253900800.

The previous prime is 961264793. The next prime is 961264807. The reversal of 961264800 is 8462169.

961264800 is a `hidden beast` number, since 9 + 6 + 1 + 2 + 648 + 0 + 0 = 666.

961264800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (961264793) and next prime (961264807).

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 (36).

It is not an unprimeable number, because it can be changed into a prime (961264807) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 4125484 + ... + 4125716.

It is an arithmetic number, because the mean of its divisors is an integer number (12186720).

Almost surely, 2^961264800 is an apocalyptic number.

961264800 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 961264800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1754887680).

961264800 is an abundant number, since it is smaller than the sum of its proper divisors (2548510560).

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

961264800 is a wasteful number, since it uses less digits than its factorization.

961264800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 453 (or 434 counting only the distinct ones).

The product of its (nonzero) digits is 20736, while the sum is 36.

The square root of 961264800 is about 31004.2706735701. The cubic root of 961264800 is about 986.9178708650.

The spelling of 961264800 in words is "nine hundred sixty-one million, two hundred sixty-four thousand, eight hundred".