461824000 has 224 divisors, whose sum is σ = 1288096992. Its totient is φ = 163840000.

The previous prime is 461823997. The next prime is 461824003. The reversal of 461824000 is 428164.

It is an interprime number because it is at equal distance from previous prime (461823997) and next prime (461824003).

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (461824003) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 11263980 + ... + 11264020.

It is an arithmetic number, because the mean of its divisors is an integer number (5750433).

Almost surely, 2^461824000 is an apocalyptic number.

461824000 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 461824000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (644048496).

461824000 is an abundant number, since it is smaller than the sum of its proper divisors (826272992).

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

461824000 is an equidigital number, since it uses as much as digits as its factorization.

461824000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 93 (or 59 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 25.

The square root of 461824000 is about 21490.0907396874. The cubic root of 461824000 is about 772.9632262557.

The spelling of 461824000 in words is "four hundred sixty-one million, eight hundred twenty-four thousand".