460872000 has 336 divisors, whose sum is σ = 1702960272. Its totient is φ = 118886400.

The previous prime is 460871987. The next prime is 460872001. The reversal of 460872000 is 278064.

It can be written as a sum of positive squares in 8 ways, for example, as 8714304 + 452157696 = 2952^2 + 21264^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (460872001) 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, 2663914 + ... + 2664086.

Almost surely, 2^460872000 is an apocalyptic number.

460872000 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 460872000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (851480136).

460872000 is an abundant number, since it is smaller than the sum of its proper divisors (1242088272).

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

460872000 is a wasteful number, since it uses less digits than its factorization.

460872000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 243 (or 220 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 460872000 is about 21467.9295694764. The cubic root of 460872000 is about 772.4317343138.

The spelling of 460872000 in words is "four hundred sixty million, eight hundred seventy-two thousand".