413961408 has 168 divisors, whose sum is σ = 1415948400. Its totient is φ = 118250496.

The previous prime is 413961397. The next prime is 413961481. The reversal of 413961408 is 804169314.

413961408 is a `hidden beast` number, since 4 + 1 + 39 + 614 + 0 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (168).

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

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 23 ways as a sum of consecutive naturals, for example, 82228 + ... + 87116.

Almost surely, 2^413961408 is an apocalyptic number.

413961408 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 413961408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (707974200).

413961408 is an abundant number, since it is smaller than the sum of its proper divisors (1001986992).

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

413961408 is a wasteful number, since it uses less digits than its factorization.

413961408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4924 (or 4901 counting only the distinct ones).

The product of its (nonzero) digits is 20736, while the sum is 36.

The square root of 413961408 is about 20346.0415806122. The cubic root of 413961408 is about 745.2808322212.

The spelling of 413961408 in words is "four hundred thirteen million, nine hundred sixty-one thousand, four hundred eight".