38209766400 has 396 divisors, whose sum is σ = 147344361892. Its totient is φ = 9404743680.

The previous prime is 38209766383. The next prime is 38209766431. The reversal of 38209766400 is 466790283.

38209766400 is a `hidden beast` number, since 38 + 209 + 7 + 6 + 6 + 400 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 3273670656 + 34936095744 = 57216^2 + 186912^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 2988822 + ... + 3001578.

Almost surely, 2^38209766400 is an apocalyptic number.

38209766400 is a gapful number since it is divisible by the number (30) 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 38209766400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (73672180946).

38209766400 is an abundant number, since it is smaller than the sum of its proper divisors (109134595492).

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

38209766400 is a wasteful number, since it uses less digits than its factorization.

38209766400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 12806 (or 12780 counting only the distinct ones).

The product of its (nonzero) digits is 435456, while the sum is 45.

It can be divided in two parts, 38209 and 766400, that added together give a square (804609 = 897²).

The spelling of 38209766400 in words is "thirty-eight billion, two hundred nine million, seven hundred sixty-six thousand, four hundred".