413640000 has 280 divisors, whose sum is σ = 1523512320. Its totient is φ = 110016000.

The previous prime is 413639999. The next prime is 413640001. The reversal of 413640000 is 46314.

It is an interprime number because it is at equal distance from previous prime (413639999) and next prime (413640001).

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 (413640001) by changing a digit.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 1079809 + ... + 1080191.

Almost surely, 2^413640000 is an apocalyptic number.

413640000 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 413640000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (761756160).

413640000 is an abundant number, since it is smaller than the sum of its proper divisors (1109872320).

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

413640000 is an equidigital number, since it uses as much as digits as its factorization.

413640000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 424 (or 393 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 413640000 is about 20338.1415080140. The cubic root of 413640000 is about 745.0878985820.

Adding to 413640000 its reverse (46314), we get a palindrome (413686314).

The spelling of 413640000 in words is "four hundred thirteen million, six hundred forty thousand".