459950400 has 756 divisors, whose sum is σ = 2098011552. Its totient is φ = 97044480.

The previous prime is 459950399. The next prime is 459950417. The reversal of 459950400 is 4059954.

It is a tau number, because it is divible by the number of its divisors (756).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 35380794 + ... + 35380806.

Almost surely, 2^459950400 is an apocalyptic number.

459950400 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 459950400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1049005776).

459950400 is an abundant number, since it is smaller than the sum of its proper divisors (1638061152).

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

459950400 is a wasteful number, since it uses less digits than its factorization.

459950400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 70 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 32400, while the sum is 36.

The square root of 459950400 is about 21446.4542523933. The cubic root of 459950400 is about 771.9165166958.

459950400 divided by its product of nonzero digits (32400) gives a triangular number (14196 = T₁₆₈).

The spelling of 459950400 in words is "four hundred fifty-nine million, nine hundred fifty thousand, four hundred".