199744000 has 80 divisors (see below), whose sum is σ = 498233736. Its totient is φ = 79872000.

The previous prime is 199743961. The next prime is 199744009. The reversal of 199744000 is 447991.

199744000 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 4 ways, for example, as 7311616 + 192432384 = 2704^2 + 13872^2 .

It is a tau number, because it is divible by the number of its divisors (80).

It is not an unprimeable number, because it can be changed into a prime (199744009) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 62440 + ... + 65560.

Almost surely, 2^199744000 is an apocalyptic number.

199744000 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 199744000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (249116868).

199744000 is an abundant number, since it is smaller than the sum of its proper divisors (298489736).

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

199744000 is an frugal number, since it uses more digits than its factorization.

199744000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3154 (or 3128 counting only the distinct ones).

The product of its (nonzero) digits is 9072, while the sum is 34.

The square root of 199744000 is about 14133.0817587673. The cubic root of 199744000 is about 584.5539249262.

The spelling of 199744000 in words is "one hundred ninety-nine million, seven hundred forty-four thousand".