413671680 has 216 divisors, whose sum is σ = 1446845400. Its totient is φ = 109117440.

The previous prime is 413671679. The next prime is 413671691. The reversal of 413671680 is 86176314.

It can be written as a sum of positive squares in 4 ways, for example, as 22581504 + 391090176 = 4752^2 + 19776^2 .

It is a super-2 number, since 2×413671680² = 342248517668044800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a nialpdrome in base 12.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1716360 + ... + 1716600.

Almost surely, 2^413671680 is an apocalyptic number.

413671680 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 413671680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (723422700).

413671680 is an abundant number, since it is smaller than the sum of its proper divisors (1033173720).

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

413671680 is a wasteful number, since it uses less digits than its factorization.

413671680 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 417 (or 400 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The square root of 413671680 is about 20338.9203253270. The cubic root of 413671680 is about 745.1069197776.

The spelling of 413671680 in words is "four hundred thirteen million, six hundred seventy-one thousand, six hundred eighty".