415905408 has 128 divisors (see below), whose sum is σ = 1299888000. Its totient is φ = 130461696.

The previous prime is 415905407. The next prime is 415905437. The reversal of 415905408 is 804509514.

It is a tau number, because it is divible by the number of its divisors (128).

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

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

It is not an unprimeable number, because it can be changed into a prime (415905407) by changing a digit.

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 15 ways as a sum of consecutive naturals, for example, 55213 + ... + 62291.

It is an arithmetic number, because the mean of its divisors is an integer number (10155375).

Almost surely, 2^415905408 is an apocalyptic number.

415905408 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 415905408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (649944000).

415905408 is an abundant number, since it is smaller than the sum of its proper divisors (883982592).

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

415905408 is a wasteful number, since it uses less digits than its factorization.

415905408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7119 (or 7101 counting only the distinct ones).

The product of its (nonzero) digits is 28800, while the sum is 36.

The square root of 415905408 is about 20393.7590453550. The cubic root of 415905408 is about 746.4456460334.

The spelling of 415905408 in words is "four hundred fifteen million, nine hundred five thousand, four hundred eight".