416419781760 has 640 divisors, whose sum is σ = 1587046919040. Its totient is φ = 103686635520.

The previous prime is 416419781759. The next prime is 416419781851. The reversal of 416419781760 is 67187914614.

416419781760 is a `hidden beast` number, since 416 + 4 + 1 + 97 + 81 + 7 + 60 = 666.

It is a tau number, because it is divible by the number of its divisors (640).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a junction number, because it is equal to n+sod(n) for n = 416419781697 and 416419781706.

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, 115445877 + ... + 115449483.

It is an arithmetic number, because the mean of its divisors is an integer number (2479760811).

Almost surely, 2^416419781760 is an apocalyptic number.

416419781760 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 416419781760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (793523459520).

416419781760 is an abundant number, since it is smaller than the sum of its proper divisors (1170627137280).

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

416419781760 is a wasteful number, since it uses less digits than its factorization.

416419781760 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3786 (or 3765 counting only the distinct ones).

The product of its (nonzero) digits is 2032128, while the sum is 54.

The spelling of 416419781760 in words is "four hundred sixteen billion, four hundred nineteen million, seven hundred eighty-one thousand, seven hundred sixty".