12414416400 has 225 divisors, whose sum is σ = 44626438461. Its totient is φ = 3305162880.

The previous prime is 12414416389. The next prime is 12414416407. The reversal of 12414416400 is 461441421.

The square root of 12414416400 is 111420.

It is a perfect power (a square), and thus also a powerful number.

12414416400 is a `hidden beast` number, since 1 + 2 + 4 + 14 + 4 + 1 + 640 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 4469189904 + 7945226496 = 66852^2 + 89136^2 .

It is a tau number, because it is divible by the number of its divisors (225).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (12414416407) by changing a digit.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 20055291 + ... + 20055909.

Almost surely, 2^12414416400 is an apocalyptic number.

12414416400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

12414416400 is the 111420-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 12414416400

12414416400 is an abundant number, since it is smaller than the sum of its proper divisors (32212022061).

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

12414416400 is an frugal number, since it uses more digits than its factorization.

12414416400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1268 (or 629 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

Adding to 12414416400 its reverse (461441421), we get a palindrome (12875857821).

The spelling of 12414416400 in words is "twelve billion, four hundred fourteen million, four hundred sixteen thousand, four hundred".