413310240 has 288 divisors, whose sum is σ = 1629403776. Its totient is φ = 93450240.

The previous prime is 413310199. The next prime is 413310257. The reversal of 413310240 is 42013314.

413310240 is a `hidden beast` number, since 413 + 3 + 10 + 240 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1320324 + ... + 1320636.

It is an arithmetic number, because the mean of its divisors is an integer number (5657652).

Almost surely, 2^413310240 is an apocalyptic number.

413310240 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 413310240, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (814701888).

413310240 is an abundant number, since it is smaller than the sum of its proper divisors (1216093536).

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

413310240 is a wasteful number, since it uses less digits than its factorization.

413310240 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 472 (or 461 counting only the distinct ones).

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

The square root of 413310240 is about 20330.0329561956. The cubic root of 413310240 is about 744.8898475341.

Adding to 413310240 its reverse (42013314), we get a palindrome (455323554).

The spelling of 413310240 in words is "four hundred thirteen million, three hundred ten thousand, two hundred forty".