414213806160 has 2560 divisors, whose sum is σ = 2015870976000. Its totient is φ = 75545395200.

The previous prime is 414213806131. The next prime is 414213806189. The reversal of 414213806160 is 61608312414.

414213806160 is a `hidden beast` number, since 4 + 1 + 4 + 2 + 1 + 38 + 0 + 616 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (414213806131) and next prime (414213806189).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 511 ways as a sum of consecutive naturals, for example, 2979955371 + ... + 2979955509.

It is an arithmetic number, because the mean of its divisors is an integer number (787449600).

Almost surely, 2^414213806160 is an apocalyptic number.

414213806160 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 414213806160, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1007935488000).

414213806160 is an abundant number, since it is smaller than the sum of its proper divisors (1601657169840).

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

414213806160 is a wasteful number, since it uses less digits than its factorization.

414213806160 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 262 (or 250 counting only the distinct ones).

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

The spelling of 414213806160 in words is "four hundred fourteen billion, two hundred thirteen million, eight hundred six thousand, one hundred sixty".