1345414406400 has 729 divisors, whose sum is σ = 5022972965101. Its totient is φ = 356772833280.

The previous prime is 1345414406377. The next prime is 1345414406407. The reversal of 1345414406400 is 46044145431.

The square root of 1345414406400 is 1159920.

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

1345414406400 is a `hidden beast` number, since 1 + 3 + 4 + 5 + 4 + 1 + 4 + 4 + 0 + 640 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 484349186304 + 861065220096 = 695952^2 + 927936^2 .

It is a tau number, because it is divible by the number of its divisors (729).

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (1345414406407) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 7516281511 + ... + 7516281689.

Almost surely, 2^{1345414406400} is an apocalyptic number.

1345414406400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

1345414406400 is the 1159920-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1345414406400

1345414406400 is an abundant number, since it is smaller than the sum of its proper divisors (3677558558701).

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

1345414406400 is an frugal number, since it uses more digits than its factorization.

1345414406400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 408 (or 189 counting only the distinct ones).

The product of its (nonzero) digits is 92160, while the sum is 36.

Multiplying 1345414406400 by its sum of digits (36), we get a square (48434918630400 = 6959520²).

1345414406400 divided by its sum of digits (36) gives a square (37372622400 = 193320²).

The spelling of 1345414406400 in words is "one trillion, three hundred forty-five billion, four hundred fourteen million, four hundred six thousand, four hundred".