413736960 has 448 divisors, whose sum is σ = 1673425152. Its totient is φ = 84934656.

The previous prime is 413736959. The next prime is 413736977. The reversal of 413736960 is 69637314.

It is a tau number, because it is divible by the number of its divisors (448).

It is a super-3 number, since 3×413736960³ (a number of 27 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (39).

It is a congruent number.

It is an unprimeable number.

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 31 ways as a sum of consecutive naturals, for example, 11182062 + ... + 11182098.

It is an arithmetic number, because the mean of its divisors is an integer number (3735324).

Almost surely, 2^413736960 is an apocalyptic number.

413736960 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 413736960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (836712576).

413736960 is an abundant number, since it is smaller than the sum of its proper divisors (1259688192).

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

413736960 is a wasteful number, since it uses less digits than its factorization.

413736960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 91 (or 67 counting only the distinct ones).

The product of its (nonzero) digits is 81648, while the sum is 39.

The square root of 413736960 is about 20340.5250669691. The cubic root of 413736960 is about 745.1461119064.

The spelling of 413736960 in words is "four hundred thirteen million, seven hundred thirty-six thousand, nine hundred sixty".