205190880400 has 405 divisors, whose sum is σ = 569205353899. Its totient is φ = 71027264000.

The previous prime is 205190880383. The next prime is 205190880403. The reversal of 205190880400 is 4088091502.

The square root of 205190880400 is 452980.

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

It can be written as a sum of positive squares in 4 ways, for example, as 2820459664 + 202370420736 = 53108^2 + 449856^2 .

It is a super-3 number, since 3×205190880400³ (a number of 35 digits) contains 333 as substring.

It is a Duffinian number.

It is a self number, because there is not a number n which added to its sum of digits gives 205190880400.

It is not an unprimeable number, because it can be changed into a prime (205190880403) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 2890012365 + ... + 2890012435.

Almost surely, 2^205190880400 is an apocalyptic number.

205190880400 is a gapful number since it is divisible by the number (20) formed by its first and last digit.

205190880400 is the 452980-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 205190880400

205190880400 is an abundant number, since it is smaller than the sum of its proper divisors (364014473499).

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

205190880400 is a wasteful number, since it uses less digits than its factorization.

205190880400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 240 (or 118 counting only the distinct ones).

The product of its (nonzero) digits is 23040, while the sum is 37.

The spelling of 205190880400 in words is "two hundred five billion, one hundred ninety million, eight hundred eighty thousand, four hundred".