213876000 has 288 divisors, whose sum is σ = 819222768. Its totient is φ = 52531200.

The previous prime is 213875983. The next prime is 213876007. The reversal of 213876000 is 678312.

213876000 is a `hidden beast` number, since 21 + 38 + 7 + 600 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 7551504 + 206324496 = 2748^2 + 14364^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is not an unprimeable number, because it can be changed into a prime (213876007) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 467772 + ... + 468228.

Almost surely, 2^213876000 is an apocalyptic number.

213876000 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

It is a pronic number, being equal to 14624×14625.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 213876000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (409611384).

213876000 is an abundant number, since it is smaller than the sum of its proper divisors (605346768).

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

213876000 is a wasteful number, since it uses less digits than its factorization.

213876000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 501 (or 480 counting only the distinct ones).

The product of its (nonzero) digits is 2016, while the sum is 27.

The square root of 213876000 is about 14624.4999914527. The cubic root of 213876000 is about 598.0268515886.

The spelling of 213876000 in words is "two hundred thirteen million, eight hundred seventy-six thousand".