461617920 has 432 divisors, whose sum is σ = 1775581920. Its totient is φ = 113467392.

The previous prime is 461617913. The next prime is 461617951. The reversal of 461617920 is 29716164.

461617920 is a `hidden beast` number, since 4 + 616 + 17 + 9 + 20 = 666.

It is a tau number, because it is divible by the number of its divisors (432).

It is a super-2 number, since 2×461617920² = 426182208130252800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

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 47 ways as a sum of consecutive naturals, for example, 12476142 + ... + 12476178.

Almost surely, 2^461617920 is an apocalyptic number.

461617920 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 461617920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (887790960).

461617920 is an abundant number, since it is smaller than the sum of its proper divisors (1313964000).

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

461617920 is a wasteful number, since it uses less digits than its factorization.

461617920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 105 (or 66 counting only the distinct ones).

The product of its (nonzero) digits is 18144, while the sum is 36.

The square root of 461617920 is about 21485.2954366469. The cubic root of 461617920 is about 772.8482358689.

The spelling of 461617920 in words is "four hundred sixty-one million, six hundred seventeen thousand, nine hundred twenty".