461829816 has 256 divisors, whose sum is σ = 1548288000. Its totient is φ = 124778880.

The previous prime is 461829793. The next prime is 461829817. The reversal of 461829816 is 618928164.

461829816 is a `hidden beast` number, since 4 + 618 + 29 + 8 + 1 + 6 = 666.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (461829817) 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 63 ways as a sum of consecutive naturals, for example, 2765365 + ... + 2765531.

It is an arithmetic number, because the mean of its divisors is an integer number (6048000).

Almost surely, 2^461829816 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 461829816, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (774144000).

461829816 is an abundant number, since it is smaller than the sum of its proper divisors (1086458184).

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

461829816 is a wasteful number, since it uses less digits than its factorization.

461829816 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 279 (or 269 counting only the distinct ones).

The product of its digits is 165888, while the sum is 45.

The square root of 461829816 is about 21490.2260574430. The cubic root of 461829816 is about 772.9664710237.

The spelling of 461829816 in words is "four hundred sixty-one million, eight hundred twenty-nine thousand, eight hundred sixteen".