261193766400 has 2400 divisors, whose sum is σ = 1226699432640. Its totient is φ = 53508833280.

The previous prime is 261193766389. The next prime is 261193766401. The reversal of 261193766400 is 4667391162.

261193766400 is a `hidden beast` number, since 261 + 19 + 376 + 6 + 4 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2400).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (261193766401) by changing a digit.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 3577996764 + ... + 3577996836.

Almost surely, 2^261193766400 is an apocalyptic number.

261193766400 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 261193766400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (613349716320).

261193766400 is an abundant number, since it is smaller than the sum of its proper divisors (965505666240).

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

261193766400 is a wasteful number, since it uses less digits than its factorization.

261193766400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 166 (or 136 counting only the distinct ones).

The product of its (nonzero) digits is 326592, while the sum is 45.

The spelling of 261193766400 in words is "two hundred sixty-one billion, one hundred ninety-three million, seven hundred sixty-six thousand, four hundred".