413488800 has 252 divisors, whose sum is σ = 1515586590. Its totient is φ = 110108160.

The previous prime is 413488741. The next prime is 413488843. The reversal of 413488800 is 8884314.

It can be written as a sum of positive squares in 3 ways, for example, as 225360144 + 188128656 = 15012^2 + 13716^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 41 ways as a sum of consecutive naturals, for example, 582846 + ... + 583554.

Almost surely, 2^413488800 is an apocalyptic number.

413488800 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 413488800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (757793295).

413488800 is an abundant number, since it is smaller than the sum of its proper divisors (1102097790).

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

413488800 is an equidigital number, since it uses as much as digits as its factorization.

413488800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 747 (or 719 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 36.

The square root of 413488800 is about 20334.4240144637. The cubic root of 413488800 is about 744.9971022214.

The spelling of 413488800 in words is "four hundred thirteen million, four hundred eighty-eight thousand, eight hundred".