413933683968 has 576 divisors, whose sum is σ = 1461476352000. Its totient is φ = 113091158016.

The previous prime is 413933683957. The next prime is 413933683991. The reversal of 413933683968 is 869386339314.

413933683968 is a `hidden beast` number, since 4 + 139 + 336 + 83 + 96 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (576).

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

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 63 ways as a sum of consecutive naturals, for example, 105620313 + ... + 105624231.

Almost surely, 2^413933683968 is an apocalyptic number.

413933683968 is a gapful number since it is divisible by the number (48) 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 413933683968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (730738176000).

413933683968 is an abundant number, since it is smaller than the sum of its proper divisors (1047542668032).

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

413933683968 is a wasteful number, since it uses less digits than its factorization.

413933683968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4047 (or 4027 counting only the distinct ones).

The product of its digits is 60466176, while the sum is 63.

It can be divided in two parts, 413933 and 683968, that added together give a palindrome (1097901).

The spelling of 413933683968 in words is "four hundred thirteen billion, nine hundred thirty-three million, six hundred eighty-three thousand, nine hundred sixty-eight".