40564414800 has 1350 divisors, whose sum is σ = 186652091262. Its totient is φ = 8108190720.

The previous prime is 40564414783. The next prime is 40564414817. The reversal of 40564414800 is 841446504.

It is a happy number.

40564414800 is a `hidden beast` number, since 4 + 0 + 5 + 644 + 1 + 4 + 8 + 0 + 0 = 666.

40564414800 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (40564414783) and next prime (40564414817).

It can be written as a sum of positive squares in 3 ways, for example, as 124813584 + 40439601216 = 11172^2 + 201096^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 269 ways as a sum of consecutive naturals, for example, 2134969191 + ... + 2134969209.

Almost surely, 2^40564414800 is an apocalyptic number.

40564414800 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 40564414800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (93326045631).

40564414800 is an abundant number, since it is smaller than the sum of its proper divisors (146087676462).

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

40564414800 is a wasteful number, since it uses less digits than its factorization.

40564414800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 103 (or 49 counting only the distinct ones).

The product of its (nonzero) digits is 61440, while the sum is 36.

The spelling of 40564414800 in words is "forty billion, five hundred sixty-four million, four hundred fourteen thousand, eight hundred".