7838638401600 has 672 divisors, whose sum is σ = 28967352458880. Its totient is φ = 2087426764800.

The previous prime is 7838638401577. The next prime is 7838638401617. The reversal of 7838638401600 is 61048368387.

7838638401600 is a `hidden beast` number, since 78 + 3 + 86 + 38 + 401 + 60 + 0 = 666.

It is a super-2 number, since 2×7838638401600² (a number of 27 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 4097562244 + ... + 4097564156.

Almost surely, 2^{7838638401600} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 7838638401600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (14483676229440).

7838638401600 is an abundant number, since it is smaller than the sum of its proper divisors (21128714057280).

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

7838638401600 is a wasteful number, since it uses less digits than its factorization.

7838638401600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3127 (or 3094 counting only the distinct ones).

The product of its (nonzero) digits is 4644864, while the sum is 54.

The spelling of 7838638401600 in words is "seven trillion, eight hundred thirty-eight billion, six hundred thirty-eight million, four hundred one thousand, six hundred".