461968502400 has 432 divisors, whose sum is σ = 1694309779890. Its totient is φ = 119851868160.

The previous prime is 461968502383. The next prime is 461968502417. The reversal of 461968502400 is 4205869164.

461968502400 is a `hidden beast` number, since 4 + 6 + 196 + 8 + 50 + 2 + 400 = 666.

It is an interprime number because it is at equal distance from previous prime (461968502383) and next prime (461968502417).

It can be written as a sum of positive squares in 9 ways, for example, as 53095219776 + 408873282624 = 230424^2 + 639432^2 .

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 39421342 + ... + 39433058.

Almost surely, 2^461968502400 is an apocalyptic number.

461968502400 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 461968502400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (847154889945).

461968502400 is an abundant number, since it is smaller than the sum of its proper divisors (1232341277490).

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

461968502400 is a wasteful number, since it uses less digits than its factorization.

461968502400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 11821 (or 11764 counting only the distinct ones).

The product of its (nonzero) digits is 414720, while the sum is 45.

The spelling of 461968502400 in words is "four hundred sixty-one billion, nine hundred sixty-eight million, five hundred two thousand, four hundred".