199752 has 64 divisors (see below), whose sum is σ = 604800. Its totient is φ = 53760.

The previous prime is 199751. The next prime is 199753. The reversal of 199752 is 257991.

It is an interprime number because it is at equal distance from previous prime (199751) and next prime (199753).

It is a nialpdrome in base 12.

It is not an unprimeable number, because it can be changed into a prime (199751) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 4852 + ... + 4892.

It is an arithmetic number, because the mean of its divisors is an integer number (9450).

2¹⁹⁹⁷⁵² is an apocalyptic number.

199752 is a gapful number since it is divisible by the number (12) 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 199752, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (302400).

199752 is an abundant number, since it is smaller than the sum of its proper divisors (405048).

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

199752 is a wasteful number, since it uses less digits than its factorization.

199752 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 86 (or 82 counting only the distinct ones).

The product of its digits is 5670, while the sum is 33.

The square root of 199752 is about 446.9362370630. The cubic root of 199752 is about 58.4561728864.

The spelling of 199752 in words is "one hundred ninety-nine thousand, seven hundred fifty-two".