459648000 has 704 divisors, whose sum is σ = 2043724800. Its totient is φ = 99532800.

The previous prime is 459647977. The next prime is 459648001. The reversal of 459648000 is 846954.

459648000 is a `hidden beast` number, since 4 + 5 + 9 + 648 + 0 + 0 + 0 = 666.

It is a super-2 number, since 2×459648000² = 422552567808000000, which contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (459648001) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 24191991 + ... + 24192009.

Almost surely, 2^459648000 is an apocalyptic number.

459648000 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 459648000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1021862400).

459648000 is an abundant number, since it is smaller than the sum of its proper divisors (1584076800).

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

459648000 is a wasteful number, since it uses less digits than its factorization.

459648000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 70 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The square root of 459648000 is about 21439.4029767622. The cubic root of 459648000 is about 771.7473109656.

The spelling of 459648000 in words is "four hundred fifty-nine million, six hundred forty-eight thousand".