412948800 has 504 divisors, whose sum is σ = 1675587200. Its totient is φ = 98841600.

The previous prime is 412948769. The next prime is 412948801. The reversal of 412948800 is 8849214.

It is a super-2 number, since 2×412948800² = 341053422842880000, 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 (412948801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 5227161 + ... + 5227239.

Almost surely, 2^412948800 is an apocalyptic number.

412948800 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 412948800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (837793600).

412948800 is an abundant number, since it is smaller than the sum of its proper divisors (1262638400).

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

412948800 is a wasteful number, since it uses less digits than its factorization.

412948800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 132 (or 100 counting only the distinct ones).

The product of its (nonzero) digits is 18432, while the sum is 36.

The square root of 412948800 is about 20321.1417002097. The cubic root of 412948800 is about 744.6726487005.

The spelling of 412948800 in words is "four hundred twelve million, nine hundred forty-eight thousand, eight hundred".