45105264400 has 405 divisors, whose sum is σ = 132793744797. Its totient is φ = 14679705600.

The previous prime is 45105264397. The next prime is 45105264469. The reversal of 45105264400 is 446250154.

It is a happy number.

The square root of 45105264400 is 212380.

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

It can be written as a sum of positive squares in 13 ways, for example, as 33399755536 + 11705508864 = 182756^2 + 108192^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 1100128380 + ... + 1100128420.

Almost surely, 2^45105264400 is an apocalyptic number.

45105264400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

45105264400 is the 212380-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 45105264400

45105264400 is an abundant number, since it is smaller than the sum of its proper divisors (87688480397).

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

45105264400 is a wasteful number, since it uses less digits than its factorization.

45105264400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 188 (or 92 counting only the distinct ones).

The product of its (nonzero) digits is 19200, while the sum is 31.

The spelling of 45105264400 in words is "forty-five billion, one hundred five million, two hundred sixty-four thousand, four hundred".