460461350462400 has 4704 divisors, whose sum is σ = 2067490567372800. Its totient is φ = 100736649216000.

The previous prime is 460461350462357. The next prime is 460461350462401. The reversal of 460461350462400 is 4264053164064.

460461350462400 is a `hidden beast` number, since 4 + 6 + 0 + 4 + 6 + 13 + 5 + 0 + 4 + 624 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (4704).

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 (460461350462401) by changing a digit.

It is a polite number, since it can be written in 671 ways as a sum of consecutive naturals, for example, 1699119374265 + ... + 1699119374535.

Almost surely, 2^{460461350462400} is an apocalyptic number.

460461350462400 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 460461350462400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1033745283686400).

460461350462400 is an abundant number, since it is smaller than the sum of its proper divisors (1607029216910400).

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

460461350462400 is a wasteful number, since it uses less digits than its factorization.

460461350462400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 500 (or 456 counting only the distinct ones).

The product of its (nonzero) digits is 1658880, while the sum is 45.

The spelling of 460461350462400 in words is "four hundred sixty trillion, four hundred sixty-one billion, three hundred fifty million, four hundred sixty-two thousand, four hundred".