415152000 has 384 divisors, whose sum is σ = 1580061600. Its totient is φ = 107136000.

The previous prime is 415151999. The next prime is 415152007. The reversal of 415152000 is 251514.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a tau number, because it is divible by the number of its divisors (384).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415152007) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 13391985 + ... + 13392015.

Almost surely, 2^415152000 is an apocalyptic number.

415152000 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 415152000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (790030800).

415152000 is an abundant number, since it is smaller than the sum of its proper divisors (1164909600).

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

415152000 is an equidigital number, since it uses as much as digits as its factorization.

415152000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 100 (or 41 counting only the distinct ones).

The product of its (nonzero) digits is 200, while the sum is 18.

The square root of 415152000 is about 20375.2791391922. The cubic root of 415152000 is about 745.9946476147.

The spelling of 415152000 in words is "four hundred fifteen million, one hundred fifty-two thousand".