461409445905408 has 4224 divisors, whose sum is σ = 1984538529792000. Its totient is φ = 101365796044800.

The previous prime is 461409445905379. The next prime is 461409445905433. The reversal of 461409445905408 is 804509544904164.

461409445905408 is a `hidden beast` number, since 4 + 6 + 1 + 40 + 9 + 4 + 45 + 9 + 0 + 540 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (4224).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 266248958110 + ... + 266248959842.

Almost surely, 2^{461409445905408} is an apocalyptic number.

461409445905408 is a gapful number since it is divisible by the number (48) 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 461409445905408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (992269264896000).

461409445905408 is an abundant number, since it is smaller than the sum of its proper divisors (1523129083886592).

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

461409445905408 is a wasteful number, since it uses less digits than its factorization.

461409445905408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1854 (or 1819 counting only the distinct ones).

The product of its (nonzero) digits is 99532800, while the sum is 63.

The spelling of 461409445905408 in words is "four hundred sixty-one trillion, four hundred nine billion, four hundred forty-five million, nine hundred five thousand, four hundred eight".