461284761600 has 2016 divisors, whose sum is σ = 1987676780544. Its totient is φ = 105106636800.

The previous prime is 461284761599. The next prime is 461284761607. The reversal of 461284761600 is 6167482164.

461284761600 is a `hidden beast` number, since 4 + 6 + 1 + 28 + 4 + 7 + 616 + 0 + 0 = 666.

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 (461284761607) by changing a digit.

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 143 ways as a sum of consecutive naturals, for example, 14880153585 + ... + 14880153615.

It is an arithmetic number, because the mean of its divisors is an integer number (985950784).

Almost surely, 2^461284761600 is an apocalyptic number.

461284761600 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 461284761600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (993838390272).

461284761600 is an abundant number, since it is smaller than the sum of its proper divisors (1526392018944).

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

461284761600 is a wasteful number, since it uses less digits than its factorization.

461284761600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 118 (or 77 counting only the distinct ones).

The product of its (nonzero) digits is 387072, while the sum is 45.

The spelling of 461284761600 in words is "four hundred sixty-one billion, two hundred eighty-four million, seven hundred sixty-one thousand, six hundred".