413108640 has 384 divisors, whose sum is σ = 1741824000. Its totient is φ = 89330688.

The previous prime is 413108639. The next prime is 413108651. The reversal of 413108640 is 46801314.

413108640 is a `hidden beast` number, since 4 + 1 + 3 + 10 + 8 + 640 = 666.

It is a Harshad number since it is a multiple of its sum of digits (27).

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 63 ways as a sum of consecutive naturals, for example, 574201 + ... + 574919.

It is an arithmetic number, because the mean of its divisors is an integer number (4536000).

Almost surely, 2^413108640 is an apocalyptic number.

413108640 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 413108640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (870912000).

413108640 is an abundant number, since it is smaller than the sum of its proper divisors (1328715360).

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

413108640 is a wasteful number, since it uses less digits than its factorization.

413108640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 769 (or 755 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 413108640 is about 20325.0741696064. The cubic root of 413108640 is about 744.7687163987.

Adding to 413108640 its reverse (46801314), we get a palindrome (459909954).

The spelling of 413108640 in words is "four hundred thirteen million, one hundred eight thousand, six hundred forty".