413892315648 has 640 divisors, whose sum is σ = 1464281280000. Its totient is φ = 115316490240.

The previous prime is 413892315647. The next prime is 413892315667. The reversal of 413892315648 is 846513298314.

It is a happy number.

413892315648 is a `hidden beast` number, since 41 + 3 + 8 + 9 + 2 + 31 + 564 + 8 = 666.

It is a super-3 number, since 3×413892315648³ (a number of 36 digits) contains 333 as substring.

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 = 413892315594 and 413892315603.

It is not an unprimeable number, because it can be changed into a prime (413892315647) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 194405848 + ... + 194407976.

It is an arithmetic number, because the mean of its divisors is an integer number (2287939500).

Almost surely, 2^413892315648 is an apocalyptic number.

413892315648 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 413892315648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (732140640000).

413892315648 is an abundant number, since it is smaller than the sum of its proper divisors (1050388964352).

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

413892315648 is an equidigital number, since it uses as much as digits as its factorization.

413892315648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2218 (or 2182 counting only the distinct ones).

The product of its digits is 4976640, while the sum is 54.

The spelling of 413892315648 in words is "four hundred thirteen billion, eight hundred ninety-two million, three hundred fifteen thousand, six hundred forty-eight".