205210000800 has 1512 divisors, whose sum is σ = 899413121376. Its totient is φ = 45539988480.

The previous prime is 205210000777. The next prime is 205210000819. The reversal of 205210000800 is 8000012502.

It is a tau number, because it is divible by the number of its divisors (1512).

It is a super-2 number, since 2×205210000800² (a number of 23 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 251 ways as a sum of consecutive naturals, for example, 1228802317 + ... + 1228802483.

It is an arithmetic number, because the mean of its divisors is an integer number (594849948).

Almost surely, 2^205210000800 is an apocalyptic number.

205210000800 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 205210000800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (449706560688).

205210000800 is an abundant number, since it is smaller than the sum of its proper divisors (694203120576).

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

205210000800 is a wasteful number, since it uses less digits than its factorization.

205210000800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 262 (or 227 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The spelling of 205210000800 in words is "two hundred five billion, two hundred ten million, eight hundred", and thus it is an aban number.