413510000640 has 896 divisors, whose sum is σ = 1543678083072. Its totient is φ = 93514629120.

The previous prime is 413510000627. The next prime is 413510000647. The reversal of 413510000640 is 46000015314.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a self number, because there is not a number n which added to its sum of digits gives 413510000640.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413510000647) by changing a digit.

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, 1461165939 + ... + 1461166221.

Almost surely, 2^413510000640 is an apocalyptic number.

413510000640 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 413510000640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (771839041536).

413510000640 is an abundant number, since it is smaller than the sum of its proper divisors (1130168082432).

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

413510000640 is a wasteful number, since it uses less digits than its factorization.

413510000640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 398 (or 374 counting only the distinct ones).

The product of its (nonzero) digits is 1440, while the sum is 24.

Adding to 413510000640 its reverse (46000015314), we get a palindrome (459510015954).

The spelling of 413510000640 in words is "four hundred thirteen billion, five hundred ten million, six hundred forty", and thus it is an aban number.