407116800 has 528 divisors, whose sum is σ = 1624499200. Its totient is φ = 99532800.

The previous prime is 407116789. The next prime is 407116807. The reversal of 407116800 is 8611704.

It is a happy number.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (407116807) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 13132785 + ... + 13132815.

Almost surely, 2^407116800 is an apocalyptic number.

407116800 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 407116800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (812249600).

407116800 is an abundant number, since it is smaller than the sum of its proper divisors (1217382400).

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

407116800 is a wasteful number, since it uses less digits than its factorization.

407116800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 89 (or 60 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 27.

The square root of 407116800 is about 20177.1355747044. The cubic root of 407116800 is about 741.1503899053.

The spelling of 407116800 in words is "four hundred seven million, one hundred sixteen thousand, eight hundred".