205689460900 has 729 divisors, whose sum is σ = 622386916641. Its totient is φ = 58777488000.

The previous prime is 205689460883. The next prime is 205689460927. The reversal of 205689460900 is 9064986502.

The square root of 205689460900 is 453530.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 74048205924 + 131641254976 = 272118^2 + 362824^2 .

It is a Harshad number since it is a multiple of its sum of digits (49).

It is an unprimeable number.

It is a polite number, since it can be written in 242 ways as a sum of consecutive naturals, for example, 6635143885 + ... + 6635143915.

Almost surely, 2^205689460900 is an apocalyptic number.

205689460900 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

205689460900 is the 453530-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 205689460900

205689460900 is an abundant number, since it is smaller than the sum of its proper divisors (416697455741).

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

205689460900 is a wasteful number, since it uses less digits than its factorization.

205689460900 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 150 (or 75 counting only the distinct ones).

The product of its (nonzero) digits is 933120, while the sum is 49.

Multiplying 205689460900 by its sum of digits (49), we get a square (10078783584100 = 3174710²).

205689460900 divided by its sum of digits (49) gives a square (4197744100 = 64790²).

The spelling of 205689460900 in words is "two hundred five billion, six hundred eighty-nine million, four hundred sixty thousand, nine hundred".