213316416000 has 400 divisors, whose sum is σ = 794612590200. Its totient is φ = 56882995200.

The previous prime is 213316415929. The next prime is 213316416031. The reversal of 213316416000 is 614613312.

213316416000 is a `hidden beast` number, since 2 + 1 + 3 + 3 + 16 + 41 + 600 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 24321026304 + 188995389696 = 155952^2 + 434736^2 .

It is a tau number, because it is divible by the number of its divisors (400).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 5163426 + ... + 5204574.

Almost surely, 2^213316416000 is an apocalyptic number.

213316416000 is a gapful number since it is divisible by the number (20) 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 213316416000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (397306295100).

213316416000 is an abundant number, since it is smaller than the sum of its proper divisors (581296174200).

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

213316416000 is an frugal number, since it uses more digits than its factorization.

213316416000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 41194 (or 41159 counting only the distinct ones).

The product of its (nonzero) digits is 2592, while the sum is 27.

The spelling of 213316416000 in words is "two hundred thirteen billion, three hundred sixteen million, four hundred sixteen thousand".