413848512000 has 2880 divisors, whose sum is σ = 1998031546368. Its totient is φ = 81285120000.

The previous prime is 413848511987. The next prime is 413848512013. The reversal of 413848512000 is 215848314.

413848512000 is a `hidden beast` number, since 4 + 138 + 4 + 8 + 512 + 0 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (413848511987) and next prime (413848512013).

It is a tau number, because it is divible by the number of its divisors (2880).

It is a super-2 number, since 2×413848512000² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 9624383979 + ... + 9624384021.

Almost surely, 2^413848512000 is an apocalyptic number.

413848512000 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 413848512000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (999015773184).

413848512000 is an abundant number, since it is smaller than the sum of its proper divisors (1584183034368).

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

413848512000 is a wasteful number, since it uses less digits than its factorization.

413848512000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 138 (or 102 counting only the distinct ones).

The product of its (nonzero) digits is 30720, while the sum is 36.

The spelling of 413848512000 in words is "four hundred thirteen billion, eight hundred forty-eight million, five hundred twelve thousand".