415150400 has 168 divisors, whose sum is σ = 1182233856. Its totient is φ = 140544000.

The previous prime is 415150363. The next prime is 415150433. The reversal of 415150400 is 4051514.

It is a super-3 number, since 3×415150400³ (a number of 27 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1131017 + ... + 1131383.

Almost surely, 2^415150400 is an apocalyptic number.

415150400 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 415150400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (591116928).

415150400 is an abundant number, since it is smaller than the sum of its proper divisors (767083456).

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

415150400 is a wasteful number, since it uses less digits than its factorization.

415150400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 497 (or 482 counting only the distinct ones).

The product of its (nonzero) digits is 400, while the sum is 20.

The square root of 415150400 is about 20375.2398758886. The cubic root of 415150400 is about 745.9936892565.

The spelling of 415150400 in words is "four hundred fifteen million, one hundred fifty thousand, four hundred".