414406520 has 128 divisors (see below), whose sum is σ = 1076198400. Its totient is φ = 142195200.

The previous prime is 414406519. The next prime is 414406529. The reversal of 414406520 is 25604414.

It is a self number, because there is not a number n which added to its sum of digits gives 414406520.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414406529) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 599375 + ... + 600065.

It is an arithmetic number, because the mean of its divisors is an integer number (8407800).

Almost surely, 2^414406520 is an apocalyptic number.

414406520 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 414406520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (538099200).

414406520 is an abundant number, since it is smaller than the sum of its proper divisors (661791880).

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

414406520 is a wasteful number, since it uses less digits than its factorization.

414406520 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 789 (or 785 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 26.

The square root of 414406520 is about 20356.9771822832. The cubic root of 414406520 is about 745.5478576069.

The spelling of 414406520 in words is "four hundred fourteen million, four hundred six thousand, five hundred twenty".