414408960 has 360 divisors, whose sum is σ = 1697631936. Its totient is φ = 94556160.

The previous prime is 414408947. The next prime is 414408989. The reversal of 414408960 is 69804414.

It is a happy number.

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

It is a super-2 number, since 2×414408960² = 343469572256563200, which contains 22 as substring.

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 39 ways as a sum of consecutive naturals, for example, 725475 + ... + 726045.

Almost surely, 2^414408960 is an apocalyptic number.

414408960 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 414408960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (848815968).

414408960 is an abundant number, since it is smaller than the sum of its proper divisors (1283222976).

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

414408960 is an equidigital number, since it uses as much as digits as its factorization.

414408960 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 611 (or 588 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 414408960 is about 20357.0371125073. The cubic root of 414408960 is about 745.5493208507.

The spelling of 414408960 in words is "four hundred fourteen million, four hundred eight thousand, nine hundred sixty".