414332531040000 has 720 divisors, whose sum is σ = 1387460486522880. Its totient is φ = 109728921600000.

The previous prime is 414332531039879. The next prime is 414332531040053. The reversal of 414332531040000 is 40135233414.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a self number, because there is not a number n which added to its sum of digits gives 414332531040000.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 152384158641 + ... + 152384161359.

It is an arithmetic number, because the mean of its divisors is an integer number (1927028453504).

Almost surely, 2^{414332531040000} is an apocalyptic number.

414332531040000 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 414332531040000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (693730243261440).

414332531040000 is an abundant number, since it is smaller than the sum of its proper divisors (973127955482880).

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

414332531040000 is a wasteful number, since it uses less digits than its factorization.

414332531040000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4826 (or 4797 counting only the distinct ones).

The product of its (nonzero) digits is 17280, while the sum is 30.

Adding to 414332531040000 its reverse (40135233414), we get a palindrome (414372666273414).

The spelling of 414332531040000 in words is "four hundred fourteen trillion, three hundred thirty-two billion, five hundred thirty-one million, forty thousand".