416487117312 has 360 divisors, whose sum is σ = 1436076077436. Its totient is φ = 115777880064.

The previous prime is 416487117289. The next prime is 416487117407. The reversal of 416487117312 is 213711784614.

416487117312 is a `hidden beast` number, since 41 + 6 + 487 + 117 + 3 + 12 = 666.

It can be written as a sum of positive squares in 2 ways, for example, as 415746406656 + 740710656 = 644784^2 + 27216^2 .

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 8329378 + ... + 8379230.

Almost surely, 2^416487117312 is an apocalyptic number.

416487117312 is a gapful number since it is divisible by the number (42) 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 416487117312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (718038038718).

416487117312 is an abundant number, since it is smaller than the sum of its proper divisors (1019588960124).

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

416487117312 is a wasteful number, since it uses less digits than its factorization.

416487117312 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 49928 (or 49902 counting only the distinct ones).

The product of its digits is 225792, while the sum is 45.

The spelling of 416487117312 in words is "four hundred sixteen billion, four hundred eighty-seven million, one hundred seventeen thousand, three hundred twelve".