101838542400 has 756 divisors, whose sum is σ = 425519857620. Its totient is φ = 23030784000.

The previous prime is 101838542387. The next prime is 101838542431. The reversal of 101838542400 is 4245838101.

101838542400 is a `hidden beast` number, since 101 + 8 + 3 + 8 + 542 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 1232852544 + 100605689856 = 35112^2 + 317184^2 .

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

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 107 ways as a sum of consecutive naturals, for example, 71264886 + ... + 71266314.

Almost surely, 2^101838542400 is an apocalyptic number.

101838542400 is a gapful number since it is divisible by the number (10) 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 101838542400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (212759928810).

101838542400 is an abundant number, since it is smaller than the sum of its proper divisors (323681315220).

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

101838542400 is a wasteful number, since it uses less digits than its factorization.

101838542400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1572 (or 1547 counting only the distinct ones).

The product of its (nonzero) digits is 30720, while the sum is 36.

The spelling of 101838542400 in words is "one hundred one billion, eight hundred thirty-eight million, five hundred forty-two thousand, four hundred".