406414800 has 360 divisors, whose sum is σ = 1595106240. Its totient is φ = 98208000.

The previous prime is 406414777. The next prime is 406414819. The reversal of 406414800 is 8414604.

It is a tau number, because it is divible by the number of its divisors (360).

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 pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1306645 + ... + 1306955.

Almost surely, 2^406414800 is an apocalyptic number.

406414800 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 406414800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (797553120).

406414800 is an abundant number, since it is smaller than the sum of its proper divisors (1188691440).

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

406414800 is a wasteful number, since it uses less digits than its factorization.

406414800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 360 (or 332 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 406414800 is about 20159.7321410777. The cubic root of 406414800 is about 740.7241511223.

The spelling of 406414800 in words is "four hundred six million, four hundred fourteen thousand, eight hundred".