413864640 has 280 divisors, whose sum is σ = 1683239712. Its totient is φ = 94556160.

The previous prime is 413864623. The next prime is 413864681. The reversal of 413864640 is 46468314.

413864640 is a `hidden beast` number, since 4 + 1 + 3 + 8 + 6 + 4 + 640 = 666.

It is a tau number, because it is divible by the number of its divisors (280).

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

It is a junction number, because it is equal to n+sod(n) for n = 413864595 and 413864604.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 180300 + ... + 182580.

Almost surely, 2^413864640 is an apocalyptic number.

413864640 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 413864640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (841619856).

413864640 is an abundant number, since it is smaller than the sum of its proper divisors (1269375072).

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

413864640 is a wasteful number, since it uses less digits than its factorization.

413864640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2317 (or 2298 counting only the distinct ones).

The product of its (nonzero) digits is 55296, while the sum is 36.

The square root of 413864640 is about 20343.6633869124. The cubic root of 413864640 is about 745.2227551843. Note that the first 3 decimals are identical.

The spelling of 413864640 in words is "four hundred thirteen million, eight hundred sixty-four thousand, six hundred forty".