90172800 has 288 divisors, whose sum is σ = 335424960. Its totient is φ = 23040000.

The previous prime is 90172751. The next prime is 90172807. The reversal of 90172800 is 827109.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×90172800² = 16262267719680000, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (90172807) 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, 892750 + ... + 892850.

It is an arithmetic number, because the mean of its divisors is an integer number (1164670).

Almost surely, 2^90172800 is an apocalyptic number.

90172800 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 90172800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (167712480).

90172800 is an abundant number, since it is smaller than the sum of its proper divisors (245252160).

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

90172800 is a wasteful number, since it uses less digits than its factorization.

90172800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 162 (or 142 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 27.

The square root of 90172800 is about 9495.9359728254. The cubic root of 90172800 is about 448.4271011967.

Adding to 90172800 its reverse (827109), we get a palindrome (90999909).

The spelling of 90172800 in words is "ninety million, one hundred seventy-two thousand, eight hundred".