415008 has 72 divisors (see below), whose sum is σ = 1297296. Its totient is φ = 124800.

The previous prime is 414991. The next prime is 415013. The reversal of 415008 is 800514.

It is a tau number, because it is divible by the number of its divisors (72).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 16.

It is an unprimeable number.

415008 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 3103 + ... + 3233.

It is an arithmetic number, because the mean of its divisors is an integer number (18018).

2⁴¹⁵⁰⁰⁸ is an apocalyptic number.

415008 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 415008, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (648648).

415008 is an abundant number, since it is smaller than the sum of its proper divisors (882288).

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

415008 is a wasteful number, since it uses less digits than its factorization.

415008 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 158 (or 147 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 415008 is about 644.2111455105. The cubic root of 415008 is about 74.5908385513.

The spelling of 415008 in words is "four hundred fifteen thousand, eight".