4661585510400 has 2160 divisors, whose sum is σ = 21365107483104. Its totient is φ = 978447237120.

The previous prime is 4661585510359. The next prime is 4661585510441. The reversal of 4661585510400 is 40155851664.

4661585510400 is a `hidden beast` number, since 4 + 6 + 6 + 1 + 58 + 551 + 0 + 40 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (4661585510359) and next prime (4661585510441).

It is a tau number, because it is divible by the number of its divisors (2160).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 24153292704 + ... + 24153292896.

Almost surely, 2^{4661585510400} is an apocalyptic number.

4661585510400 is a gapful number since it is divisible by the number (40) 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 4661585510400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10682553741552).

4661585510400 is an abundant number, since it is smaller than the sum of its proper divisors (16703521972704).

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

4661585510400 is an equidigital number, since it uses as much as digits as its factorization.

4661585510400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 269 (or 223 counting only the distinct ones).

The product of its (nonzero) digits is 576000, while the sum is 45.

The spelling of 4661585510400 in words is "four trillion, six hundred sixty-one billion, five hundred eighty-five million, five hundred ten thousand, four hundred".