416352000 has 144 divisors (see below), whose sum is σ = 1383232032. Its totient is φ = 111001600.

The previous prime is 416351993. The next prime is 416352029. The reversal of 416352000 is 253614.

It is a happy number.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 93832 + ... + 98168.

It is an arithmetic number, because the mean of its divisors is an integer number (9605778).

Almost surely, 2^416352000 is an apocalyptic number.

416352000 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 416352000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (691616016).

416352000 is an abundant number, since it is smaller than the sum of its proper divisors (966880032).

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

416352000 is an equidigital number, since it uses as much as digits as its factorization.

416352000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4371 (or 4347 counting only the distinct ones).

The product of its (nonzero) digits is 720, while the sum is 21.

The square root of 416352000 is about 20404.7053397004. The cubic root of 416352000 is about 746.7127239163.

The spelling of 416352000 in words is "four hundred sixteen million, three hundred fifty-two thousand".