40409040400 has 225 divisors, whose sum is σ = 107118577101. Its totient is φ = 14647121280.

The previous prime is 40409040379. The next prime is 40409040401. The reversal of 40409040400 is 404090404.

The square root of 40409040400 is 201020.

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

It can be written as a sum of positive squares in only one way, i.e., 14547254544 + 25861785856 = 120612^2 + 160816^2 .

It is a Harshad number since it is a multiple of its sum of digits (25).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (40409040401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 1756914789 + ... + 1756914811.

Almost surely, 2^40409040400 is an apocalyptic number.

40409040400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

40409040400 is the 201020-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 40409040400

40409040400 is an abundant number, since it is smaller than the sum of its proper divisors (66709536701).

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

40409040400 is an frugal number, since it uses more digits than its factorization.

40409040400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 148 (or 49 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 25.

Multiplying 40409040400 by its sum of digits (25), we get a square (1010226010000 = 1005100²).

40409040400 divided by its sum of digits (25) gives a square (1616361616 = 40204²).

Multiplying 40409040400 by its product of nonzero digits (2304), we get a square (93102429081600 = 9648960²).

40409040400 divided by its reverse (404090404) gives a square (100 = 10²).

The spelling of 40409040400 in words is "forty billion, four hundred nine million, forty thousand, four hundred".