968832000 has 396 divisors, whose sum is σ = 3615796236. Its totient is φ = 249446400.

The previous prime is 968831999. The next prime is 968832001. The reversal of 968832000 is 238869.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is an interprime number because it is at equal distance from previous prime (968831999) and next prime (968832001).

It can be written as a sum of positive squares in 6 ways, for example, as 291999744 + 676832256 = 17088^2 + 26016^2 .

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (968832001) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 33407986 + ... + 33408014.

Almost surely, 2^968832000 is an apocalyptic number.

968832000 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 968832000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1807898118).

968832000 is an abundant number, since it is smaller than the sum of its proper divisors (2646964236).

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

968832000 is a wasteful number, since it uses less digits than its factorization.

968832000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 99 (or 39 counting only the distinct ones).

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

The square root of 968832000 is about 31126.0662467971. The cubic root of 968832000 is about 989.5008196636.

The spelling of 968832000 in words is "nine hundred sixty-eight million, eight hundred thirty-two thousand".