413542400 has 144 divisors (see below), whose sum is σ = 1055674620. Its totient is φ = 160563200.

The previous prime is 413542397. The next prime is 413542421. The reversal of 413542400 is 4245314.

It can be written as a sum of positive squares in 6 ways, for example, as 164660224 + 248882176 = 12832^2 + 15776^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2099102 + ... + 2099298.

Almost surely, 2^413542400 is an apocalyptic number.

413542400 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 413542400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (527837310).

413542400 is an abundant number, since it is smaller than the sum of its proper divisors (642132220).

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

413542400 is a wasteful number, since it uses less digits than its factorization.

413542400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 270 (or 245 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 23.

The square root of 413542400 is about 20335.7419338464. The cubic root of 413542400 is about 745.0292918231.

Adding to 413542400 its reverse (4245314), we get a palindrome (417787714).

It can be divided in two parts, 4 and 13542400, that multiplied together give a square (54169600 = 7360²).

The spelling of 413542400 in words is "four hundred thirteen million, five hundred forty-two thousand, four hundred".