9752464800 has 864 divisors, whose sum is σ = 40845010752. Its totient is φ = 2249441280.

The previous prime is 9752464739. The next prime is 9752464823. The reversal of 9752464800 is 84642579.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (864).

It is a super-2 number, since 2×9752464800² (a number of 21 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 42962287 + ... + 42962513.

It is an arithmetic number, because the mean of its divisors is an integer number (47274318).

Almost surely, 2^9752464800 is an apocalyptic number.

9752464800 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 9752464800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20422505376).

9752464800 is an abundant number, since it is smaller than the sum of its proper divisors (31092545952).

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

9752464800 is a wasteful number, since it uses less digits than its factorization.

9752464800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 292 (or 267 counting only the distinct ones).

The product of its (nonzero) digits is 483840, while the sum is 45.

The square root of 9752464800 is about 98754.5685019179. The cubic root of 9752464800 is about 2136.5093470337.

It can be divided in two parts, 9752 and 464800, that added together give a cube (474552 = 78³).

The spelling of 9752464800 in words is "nine billion, seven hundred fifty-two million, four hundred sixty-four thousand, eight hundred".