38416615264800 has 1080 divisors, whose sum is σ = 152960891321700. Its totient is φ = 9370420899840.

The previous prime is 38416615264723. The next prime is 38416615264837. The reversal of 38416615264800 is 846251661483.

38416615264800 is a `hidden beast` number, since 3 + 8 + 4 + 1 + 6 + 6 + 152 + 6 + 480 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 12442466102544 + 25974149162256 = 3527388^2 + 5096484^2 .

It is a tau number, because it is divible by the number of its divisors (1080).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 179 ways as a sum of consecutive naturals, for example, 678362886 + ... + 678419514.

Almost surely, 2^{38416615264800} is an apocalyptic number.

38416615264800 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 38416615264800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (76480445660850).

38416615264800 is an abundant number, since it is smaller than the sum of its proper divisors (114544276056900).

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

38416615264800 is a wasteful number, since it uses less digits than its factorization.

38416615264800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 56728 (or 56687 counting only the distinct ones).

The product of its (nonzero) digits is 6635520, while the sum is 54.

The spelling of 38416615264800 in words is "thirty-eight trillion, four hundred sixteen billion, six hundred fifteen million, two hundred sixty-four thousand, eight hundred".