414381312000 has 384 divisors, whose sum is σ = 1531941465600. Its totient is φ = 110499840000.

The previous prime is 414381311999. The next prime is 414381312073. The reversal of 414381312000 is 213183414.

414381312000 is a `hidden beast` number, since 414 + 38 + 13 + 1 + 200 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 6882025 + ... + 6941975.

It is an arithmetic number, because the mean of its divisors is an integer number (3989430900).

Almost surely, 2^414381312000 is an apocalyptic number.

414381312000 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 414381312000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (765970732800).

414381312000 is an abundant number, since it is smaller than the sum of its proper divisors (1117560153600).

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

414381312000 is an equidigital number, since it uses as much as digits as its factorization.

414381312000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 59997 (or 59961 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

Adding to 414381312000 its reverse (213183414), we get a palindrome (414594495414).

The spelling of 414381312000 in words is "four hundred fourteen billion, three hundred eighty-one million, three hundred twelve thousand".