414400560 has 320 divisors, whose sum is σ = 1550376960. Its totient is φ = 89579520.

The previous prime is 414400559. The next prime is 414400607. The reversal of 414400560 is 65004414.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a self number, because there is not a number n which added to its sum of digits gives 414400560.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 3801786 + ... + 3801894.

It is an arithmetic number, because the mean of its divisors is an integer number (4844928).

Almost surely, 2^414400560 is an apocalyptic number.

414400560 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 414400560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (775188480).

414400560 is an abundant number, since it is smaller than the sum of its proper divisors (1135976400).

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

414400560 is a wasteful number, since it uses less digits than its factorization.

414400560 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 236 (or 230 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 24.

The square root of 414400560 is about 20356.8307946006. The cubic root of 414400560 is about 745.5442834301.

Adding to 414400560 its reverse (65004414), we get a palindrome (479404974).

The spelling of 414400560 in words is "four hundred fourteen million, four hundred thousand, five hundred sixty".