213968800 has 72 divisors (see below), whose sum is σ = 553113036. Its totient is φ = 80547840.

The previous prime is 213968761. The next prime is 213968809. The reversal of 213968800 is 8869312.

213968800 is digitally balanced in base 3, 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 6 ways, for example, as 60902416 + 153066384 = 7804^2 + 12372^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 213968800.

It is not an unprimeable number, because it can be changed into a prime (213968809) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5734 + ... + 21466.

Almost surely, 2^213968800 is an apocalyptic number.

213968800 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 213968800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (276556518).

213968800 is an abundant number, since it is smaller than the sum of its proper divisors (339144236).

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

213968800 is a wasteful number, since it uses less digits than its factorization.

213968800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 15770 (or 15757 counting only the distinct ones).

The product of its (nonzero) digits is 20736, while the sum is 37.

The square root of 213968800 is about 14627.6724054102. The cubic root of 213968800 is about 598.1133329565.

The spelling of 213968800 in words is "two hundred thirteen million, nine hundred sixty-eight thousand, eight hundred".