413181600 has 576 divisors, whose sum is σ = 1653644160. Its totient is φ = 88473600.

The previous prime is 413181599. The next prime is 413181689. The reversal of 413181600 is 6181314.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 10077580 + ... + 10077620.

It is an arithmetic number, because the mean of its divisors is an integer number (2870910).

Almost surely, 2^413181600 is an apocalyptic number.

413181600 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 413181600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (826822080).

413181600 is an abundant number, since it is smaller than the sum of its proper divisors (1240462560).

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

413181600 is a wasteful number, since it uses less digits than its factorization.

413181600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 113 (or 100 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 24.

The square root of 413181600 is about 20326.8689177650. The cubic root of 413181600 is about 744.8125588828.

It can be divided in two parts, 4131 and 81600, that multiplied together give a square (337089600 = 18360²).

The spelling of 413181600 in words is "four hundred thirteen million, one hundred eighty-one thousand, six hundred".