413436960 has 480 divisors, whose sum is σ = 1624613760. Its totient is φ = 98537472.

The previous prime is 413436901. The next prime is 413436973. The reversal of 413436960 is 69634314.

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 5663484 + ... + 5663556.

It is an arithmetic number, because the mean of its divisors is an integer number (3384612).

Almost surely, 2^413436960 is an apocalyptic number.

413436960 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 413436960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (812306880).

413436960 is an abundant number, since it is smaller than the sum of its proper divisors (1211176800).

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

413436960 is a wasteful number, since it uses less digits than its factorization.

413436960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 142 (or 125 counting only the distinct ones).

The product of its (nonzero) digits is 46656, while the sum is 36.

The square root of 413436960 is about 20333.1492887846. The cubic root of 413436960 is about 744.9659669452.

The spelling of 413436960 in words is "four hundred thirteen million, four hundred thirty-six thousand, nine hundred sixty".