101838195950400 has 1260 divisors, whose sum is σ = 468943253150988. Its totient is φ = 21486722826240.

The previous prime is 101838195950269. The next prime is 101838195950431. The reversal of 101838195950400 is 4059591838101.

It is a happy number.

101838195950400 is a `hidden beast` number, since 1 + 0 + 1 + 8 + 3 + 8 + 1 + 9 + 595 + 0 + 40 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 8480396300544 + 93357799649856 = 2912112^2 + 9662184^2 .

It is a tau number, because it is divible by the number of its divisors (1260).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 179 ways as a sum of consecutive naturals, for example, 81938412 + ... + 83171988.

Almost surely, 2^{101838195950400} is an apocalyptic number.

101838195950400 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 101838195950400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (234471626575494).

101838195950400 is an abundant number, since it is smaller than the sum of its proper divisors (367105057200588).

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

101838195950400 is a wasteful number, since it uses less digits than its factorization.

101838195950400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1233638 (or 1233607 counting only the distinct ones).

The product of its (nonzero) digits is 1555200, while the sum is 54.

The spelling of 101838195950400 in words is "one hundred one trillion, eight hundred thirty-eight billion, one hundred ninety-five million, nine hundred fifty thousand, four hundred".