413712000 has 576 divisors, whose sum is σ = 1703459160. Its totient is φ = 95846400.

The previous prime is 413711981. The next prime is 413712029. The reversal of 413712000 is 217314.

It can be written as a sum of positive squares in 12 ways, for example, as 80138304 + 333573696 = 8952^2 + 18264^2 .

It is a tau number, because it is divible by the number of its divisors (576).

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

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 24335992 + ... + 24336008.

Almost surely, 2^413712000 is an apocalyptic number.

413712000 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 413712000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (851729580).

413712000 is an abundant number, since it is smaller than the sum of its proper divisors (1289747160).

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

413712000 is a wasteful number, since it uses less digits than its factorization.

413712000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 78 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 168, while the sum is 18.

The square root of 413712000 is about 20339.9115042323. The cubic root of 413712000 is about 745.1311271675.

Adding to 413712000 its reverse (217314), we get a palindrome (413929314).

The spelling of 413712000 in words is "four hundred thirteen million, seven hundred twelve thousand".