199920 has 120 divisors (see below), whose sum is σ = 763344. Its totient is φ = 43008.

The previous prime is 199909. The next prime is 199921. The reversal of 199920 is 29991.

199920 = T₉₁ + T₉₂ + ... + T₁₂₄.

199920 = 63² + 64² + ... + 94².

199920 is nontrivially palindromic in base 13.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a zygodrome in base 2.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 199920.

It is not an unprimeable number, because it can be changed into a prime (199921) by changing a digit.

199920 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 11752 + ... + 11768.

2¹⁹⁹⁹²⁰ is an apocalyptic number.

199920 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 199920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (381672).

199920 is an abundant number, since it is smaller than the sum of its proper divisors (563424).

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

199920 is a wasteful number, since it uses less digits than its factorization.

199920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 47 (or 34 counting only the distinct ones).

The product of its (nonzero) digits is 1458, while the sum is 30.

The square root of 199920 is about 447.1241438348. The cubic root of 199920 is about 58.4725563437.

The spelling of 199920 in words is "one hundred ninety-nine thousand, nine hundred twenty".