968292000 has 288 divisors, whose sum is σ = 3702600720. Its totient is φ = 238233600.

The previous prime is 968291981. The next prime is 968292007. The reversal of 968292000 is 292869.

It can be written as a sum of positive squares in 8 ways, for example, as 39992976 + 928299024 = 6324^2 + 30468^2 .

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 a congruent number.

It is not an unprimeable number, because it can be changed into a prime (968292007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 466966 + ... + 469034.

Almost surely, 2^968292000 is an apocalyptic number.

968292000 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 968292000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1851300360).

968292000 is an abundant number, since it is smaller than the sum of its proper divisors (2734308720).

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

968292000 is a wasteful number, since it uses less digits than its factorization.

968292000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2113 (or 2092 counting only the distinct ones).

The product of its (nonzero) digits is 15552, while the sum is 36.

The square root of 968292000 is about 31117.3906361057. The cubic root of 968292000 is about 989.3169454222.

The spelling of 968292000 in words is "nine hundred sixty-eight million, two hundred ninety-two thousand".