414133340320 has 192 divisors, whose sum is σ = 1127186565120. Its totient is φ = 140846404608.

The previous prime is 414133340317. The next prime is 414133340351. The reversal of 414133340320 is 23043331414.

It is a Harshad number since it is a multiple of its sum of digits (28).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 88810309 + ... + 88814971.

It is an arithmetic number, because the mean of its divisors is an integer number (5870763360).

Almost surely, 2^414133340320 is an apocalyptic number.

414133340320 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 414133340320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (563593282560).

414133340320 is an abundant number, since it is smaller than the sum of its proper divisors (713053224800).

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

414133340320 is a wasteful number, since it uses less digits than its factorization.

414133340320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5307 (or 5299 counting only the distinct ones).

The product of its (nonzero) digits is 10368, while the sum is 28.

Adding to 414133340320 its reverse (23043331414), we get a palindrome (437176671734).

The spelling of 414133340320 in words is "four hundred fourteen billion, one hundred thirty-three million, three hundred forty thousand, three hundred twenty".