6410416334400 has 945 divisors, whose sum is σ = 25562298831993. Its totient is φ = 1575031910400.

The previous prime is 6410416334381. The next prime is 6410416334407. The reversal of 6410416334400 is 44336140146.

The square root of 6410416334400 is 2531880.

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

6410416334400 is a `hidden beast` number, since 6 + 4 + 10 + 4 + 1 + 633 + 4 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 6268293366336 + 142122968064 = 2503656^2 + 376992^2 .

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

It is not an unprimeable number, because it can be changed into a prime (6410416334407) by changing a digit.

It is a polite number, since it can be written in 134 ways as a sum of consecutive naturals, for example, 11849198130 + ... + 11849198670.

Almost surely, 2^{6410416334400} is an apocalyptic number.

6410416334400 is a gapful number since it is divisible by the number (60) formed by its first and last digit.

6410416334400 is the 2531880-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 6410416334400

6410416334400 is an abundant number, since it is smaller than the sum of its proper divisors (19151882497593).

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

6410416334400 is an equidigital number, since it uses as much as digits as its factorization.

6410416334400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1142 (or 564 counting only the distinct ones).

The product of its (nonzero) digits is 82944, while the sum is 36.

Multiplying 6410416334400 by its sum of digits (36), we get a square (230774988038400 = 15191280²).

6410416334400 divided by its sum of digits (36) gives a square (178067120400 = 421980²).

The spelling of 6410416334400 in words is "six trillion, four hundred ten billion, four hundred sixteen million, three hundred thirty-four thousand, four hundred".