412992000 has 320 divisors, whose sum is σ = 1532044800. Its totient is φ = 109670400.

The previous prime is 412991983. The next prime is 412992017. The reversal of 412992000 is 299214.

It is an interprime number because it is at equal distance from previous prime (412991983) and next prime (412992017).

It is a tau number, because it is divible by the number of its divisors (320).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 1727881 + ... + 1728119.

It is an arithmetic number, because the mean of its divisors is an integer number (4787640).

Almost surely, 2^412992000 is an apocalyptic number.

412992000 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 412992000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (766022400).

412992000 is an abundant number, since it is smaller than the sum of its proper divisors (1119052800).

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

412992000 is an equidigital number, since it uses as much as digits as its factorization.

412992000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 281 (or 249 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The square root of 412992000 is about 20322.2046048159. The cubic root of 412992000 is about 744.6986153875.

The spelling of 412992000 in words is "four hundred twelve million, nine hundred ninety-two thousand".