413780400 has 480 divisors, whose sum is σ = 1664298240. Its totient is φ = 97977600.

The previous prime is 413780383. The next prime is 413780401. The reversal of 413780400 is 4087314.

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 (413780401) by changing a digit.

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 95 ways as a sum of consecutive naturals, for example, 9622779 + ... + 9622821.

It is an arithmetic number, because the mean of its divisors is an integer number (3467288).

Almost surely, 2^413780400 is an apocalyptic number.

413780400 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 413780400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (832149120).

413780400 is an abundant number, since it is smaller than the sum of its proper divisors (1250517840).

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

413780400 is a wasteful number, since it uses less digits than its factorization.

413780400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 93 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 413780400 is about 20341.5928579844. The cubic root of 413780400 is about 745.1721896784.

The spelling of 413780400 in words is "four hundred thirteen million, seven hundred eighty thousand, four hundred".