199921824 has 192 divisors, whose sum is σ = 616896000. Its totient is φ = 62899200.

The previous prime is 199921807. The next prime is 199921831. The reversal of 199921824 is 428129991.

It is a super-2 number, since 2×199921824² = 79937471422973952, which contains 22 as substring.

It is a nude number because it is divisible by every one of its digits.

It is a self number, because there is not a number n which added to its sum of digits gives 199921824.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1979374 + ... + 1979474.

It is an arithmetic number, because the mean of its divisors is an integer number (3213000).

Almost surely, 2^199921824 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 199921824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (308448000).

199921824 is an abundant number, since it is smaller than the sum of its proper divisors (416974176).

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

199921824 is a wasteful number, since it uses less digits than its factorization.

199921824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 228 (or 214 counting only the distinct ones).

The product of its digits is 93312, while the sum is 45.

The square root of 199921824 is about 14139.3714145997. The cubic root of 199921824 is about 584.7273417090.

The spelling of 199921824 in words is "one hundred ninety-nine million, nine hundred twenty-one thousand, eight hundred twenty-four".