460948800 has 336 divisors, whose sum is σ = 1666768320. Its totient is φ = 110837760.

The previous prime is 460948739. The next prime is 460948801. The reversal of 460948800 is 8849064.

It is a Harshad number since it is a multiple of its sum of digits (39).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (460948801) by changing a digit.

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, 5179156 + ... + 5179244.

It is an arithmetic number, because the mean of its divisors is an integer number (4960620).

Almost surely, 2^460948800 is an apocalyptic number.

460948800 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 460948800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (833384160).

460948800 is an abundant number, since it is smaller than the sum of its proper divisors (1205819520).

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

460948800 is a wasteful number, since it uses less digits than its factorization.

460948800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 210 (or 195 counting only the distinct ones).

The product of its (nonzero) digits is 55296, while the sum is 39.

The square root of 460948800 is about 21469.7182096086. The cubic root of 460948800 is about 772.4746381008.

The spelling of 460948800 in words is "four hundred sixty million, nine hundred forty-eight thousand, eight hundred".