460224000 has 480 divisors, whose sum is σ = 1792492416. Its totient is φ = 113049600.

The previous prime is 460223993. The next prime is 460224001. The reversal of 460224000 is 422064.

It is a tau number, because it is divible by the number of its divisors (480).

It is a super-2 number, since 2×460224000² = 423612260352000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (460224001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 9791977 + ... + 9792023.

Almost surely, 2^460224000 is an apocalyptic number.

460224000 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 460224000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (896246208).

460224000 is an abundant number, since it is smaller than the sum of its proper divisors (1332268416).

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

460224000 is a wasteful number, since it uses less digits than its factorization.

460224000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 103 (or 74 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 18.

The square root of 460224000 is about 21452.8319808831. The cubic root of 460224000 is about 772.0695437007.

Adding to 460224000 its reverse (422064), we get a palindrome (460646064).

The spelling of 460224000 in words is "four hundred sixty million, two hundred twenty-four thousand".