463872000 has 224 divisors, whose sum is σ = 1553894784. Its totient is φ = 122880000.

The previous prime is 463871987. The next prime is 463872001. The reversal of 463872000 is 278364.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is not an unprimeable number, because it can be changed into a prime (463872001) 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, 3071925 + ... + 3072075.

Almost surely, 2^463872000 is an apocalyptic number.

463872000 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 463872000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (776947392).

463872000 is an abundant number, since it is smaller than the sum of its proper divisors (1090022784).

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

463872000 is an equidigital number, since it uses as much as digits as its factorization.

463872000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 195 (or 161 counting only the distinct ones).

The product of its (nonzero) digits is 8064, while the sum is 30.

The square root of 463872000 is about 21537.6878981937. The cubic root of 463872000 is about 774.1041330426.

The spelling of 463872000 in words is "four hundred sixty-three million, eight hundred seventy-two thousand".