409742064000 has 640 divisors, whose sum is σ = 1527304727520. Its totient is φ = 108869529600.

The previous prime is 409742063977. The next prime is 409742064007. The reversal of 409742064000 is 460247904.

409742064000 is a `hidden beast` number, since 4 + 0 + 9 + 7 + 4 + 2 + 0 + 640 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (640).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (409742064007) by changing a digit.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 605231662 + ... + 605232338.

Almost surely, 2^409742064000 is an apocalyptic number.

409742064000 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 409742064000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (763652363760).

409742064000 is an abundant number, since it is smaller than the sum of its proper divisors (1117562663520).

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

409742064000 is an equidigital number, since it uses as much as digits as its factorization.

409742064000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1185 (or 1154 counting only the distinct ones).

The product of its (nonzero) digits is 48384, while the sum is 36.

The spelling of 409742064000 in words is "four hundred nine billion, seven hundred forty-two million, sixty-four thousand".