975168000 has 240 divisors, whose sum is σ = 3514446936. Its totient is φ = 259891200.

The previous prime is 975167971. The next prime is 975168011. The reversal of 975168000 is 861579.

It can be written as a sum of positive squares in 4 ways, for example, as 234457344 + 740710656 = 15312^2 + 27216^2 .

It is a tau number, because it is divible by the number of its divisors (240).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 575154 + ... + 576846.

Almost surely, 2^975168000 is an apocalyptic number.

975168000 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 975168000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1757223468).

975168000 is an abundant number, since it is smaller than the sum of its proper divisors (2539278936).

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

975168000 is a wasteful number, since it uses less digits than its factorization.

975168000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1732 (or 1703 counting only the distinct ones).

The product of its (nonzero) digits is 15120, while the sum is 36.

The square root of 975168000 is about 31227.6800291024. The cubic root of 975168000 is about 991.6531912896.

The spelling of 975168000 in words is "nine hundred seventy-five million, one hundred sixty-eight thousand".