214016400 has 360 divisors, whose sum is σ = 850023720. Its totient is φ = 49397760.

The previous prime is 214016389. The next prime is 214016419. The reversal of 214016400 is 4610412.

214016400 is a `hidden beast` number, since 21 + 4 + 0 + 1 + 640 + 0 = 666.

214016400 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 12 ways, for example, as 119771136 + 94245264 = 10944^2 + 9708^2 .

It is a tau number, because it is divible by the number of its divisors (360).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 795466 + ... + 795734.

It is an arithmetic number, because the mean of its divisors is an integer number (2361177).

Almost surely, 2^214016400 is an apocalyptic number.

214016400 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 214016400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (425011860).

214016400 is an abundant number, since it is smaller than the sum of its proper divisors (636007320).

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

214016400 is a wasteful number, since it uses less digits than its factorization.

214016400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 323 (or 309 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 214016400 is about 14629.2993680490. The cubic root of 214016400 is about 598.1576822320.

Adding to 214016400 its reverse (4610412), we get a palindrome (218626812).

The spelling of 214016400 in words is "two hundred fourteen million, sixteen thousand, four hundred".