414417120480 has 576 divisors, whose sum is σ = 1599123435840. Its totient is φ = 100161515520.

The previous prime is 414417120451. The next prime is 414417120497. The reversal of 414417120480 is 84021714414.

414417120480 is a `hidden beast` number, since 4 + 1 + 4 + 4 + 171 + 2 + 0 + 480 = 666.

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 95 ways as a sum of consecutive naturals, for example, 207518842 + ... + 207520838.

It is an arithmetic number, because the mean of its divisors is an integer number (2776255965).

Almost surely, 2^414417120480 is an apocalyptic number.

414417120480 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 414417120480, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (799561717920).

414417120480 is an abundant number, since it is smaller than the sum of its proper divisors (1184706315360).

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

414417120480 is a wasteful number, since it uses less digits than its factorization.

414417120480 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2440 (or 2415 counting only the distinct ones).

The product of its (nonzero) digits is 28672, while the sum is 36.

Adding to 414417120480 its reverse (84021714414), we get a palindrome (498438834894).

The spelling of 414417120480 in words is "four hundred fourteen billion, four hundred seventeen million, one hundred twenty thousand, four hundred eighty".