459716400 has 720 divisors, whose sum is σ = 2014871040. Its totient is φ = 95385600.

The previous prime is 459716399. The next prime is 459716401. The reversal of 459716400 is 4617954.

459716400 is a `hidden beast` number, since 4 + 5 + 9 + 7 + 1 + 640 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (459716399) and next prime (459716401).

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×459716400² = 422678336857920000, which contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (459716401) by changing a digit.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 9781177 + ... + 9781223.

It is an arithmetic number, because the mean of its divisors is an integer number (2798432).

Almost surely, 2^459716400 is an apocalyptic number.

459716400 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 459716400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1007435520).

459716400 is an abundant number, since it is smaller than the sum of its proper divisors (1555154640).

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

459716400 is a wasteful number, since it uses less digits than its factorization.

459716400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 114 (or 100 counting only the distinct ones).

The product of its (nonzero) digits is 30240, while the sum is 36.

The square root of 459716400 is about 21440.9981110955. The cubic root of 459716400 is about 771.7855901835.

The spelling of 459716400 in words is "four hundred fifty-nine million, seven hundred sixteen thousand, four hundred".