415128000 has 336 divisors, whose sum is σ = 1599066144. Its totient is φ = 94617600.

The previous prime is 415127957. The next prime is 415128001. The reversal of 415128000 is 821514.

It is a tau number, because it is divible by the number of its divisors (336).

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415128001) 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, 1175824 + ... + 1176176.

Almost surely, 2^415128000 is an apocalyptic number.

415128000 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 415128000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (799533072).

415128000 is an abundant number, since it is smaller than the sum of its proper divisors (1183938144).

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

415128000 is a wasteful number, since it uses less digits than its factorization.

415128000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 397 (or 370 counting only the distinct ones).

The product of its (nonzero) digits is 320, while the sum is 21.

The square root of 415128000 is about 20374.6901816936. The cubic root of 415128000 is about 745.9802719832.

Adding to 415128000 its reverse (821514), we get a palindrome (415949514).

The spelling of 415128000 in words is "four hundred fifteen million, one hundred twenty-eight thousand".