416122790400 has 600 divisors, whose sum is σ = 1630764279540. Its totient is φ = 104434237440.

The previous prime is 416122790399. The next prime is 416122790407. The reversal of 416122790400 is 4097221614.

It is a happy number.

416122790400 is a `hidden beast` number, since 4 + 161 + 2 + 2 + 7 + 90 + 400 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 131786424576 + 284336365824 = 363024^2 + 533232^2 .

It is a tau number, because it is divible by the number of its divisors (600).

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

It is not an unprimeable number, because it can be changed into a prime (416122790407) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 17613796 + ... + 17637404.

Almost surely, 2^416122790400 is an apocalyptic number.

416122790400 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 416122790400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (815382139770).

416122790400 is an abundant number, since it is smaller than the sum of its proper divisors (1214641489140).

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

416122790400 is a wasteful number, since it uses less digits than its factorization.

416122790400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 23666 (or 23636 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The spelling of 416122790400 in words is "four hundred sixteen billion, one hundred twenty-two million, seven hundred ninety thousand, four hundred".