198288000 has 448 divisors, whose sum is σ = 782631720. Its totient is φ = 49766400.

The previous prime is 198287989. The next prime is 198288001. The reversal of 198288000 is 882891.

It can be written as a sum of positive squares in 4 ways, for example, as 86266944 + 112021056 = 9288^2 + 10584^2 .

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

It is not an unprimeable number, because it can be changed into a prime (198288001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 55 ways as a sum of consecutive naturals, for example, 11663992 + ... + 11664008.

Almost surely, 2^198288000 is an apocalyptic number.

198288000 is a gapful number since it is divisible by the number (10) 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 198288000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (391315860).

198288000 is an abundant number, since it is smaller than the sum of its proper divisors (584343720).

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

198288000 is an frugal number, since it uses more digits than its factorization.

198288000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 64 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 36.

The square root of 198288000 is about 14081.4771952377. The cubic root of 198288000 is about 583.1301242299.

The spelling of 198288000 in words is "one hundred ninety-eight million, two hundred eighty-eight thousand".