413624640 has 448 divisors, whose sum is σ = 1622218752. Its totient is φ = 87859200.

The previous prime is 413624579. The next prime is 413624641. The reversal of 413624640 is 46426314.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a junction number, because it is equal to n+sod(n) for n = 413624598 and 413624607.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413624641) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 3157375 + ... + 3157505.

It is an arithmetic number, because the mean of its divisors is an integer number (3621024).

Almost surely, 2^413624640 is an apocalyptic number.

413624640 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 413624640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (811109376).

413624640 is an abundant number, since it is smaller than the sum of its proper divisors (1208594112).

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

413624640 is a wasteful number, since it uses less digits than its factorization.

413624640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 198 (or 188 counting only the distinct ones).

The product of its (nonzero) digits is 13824, while the sum is 30.

The square root of 413624640 is about 20337.7638888841. The cubic root of 413624640 is about 745.0786758345.

The spelling of 413624640 in words is "four hundred thirteen million, six hundred twenty-four thousand, six hundred forty".