105253149081600 has 3024 divisors, whose sum is σ = 445266563449344. Its totient is φ = 24461180928000.

The previous prime is 105253149081571. The next prime is 105253149081637. The reversal of 105253149081600 is 6180941352501.

It is a happy number.

105253149081600 is a `hidden beast` number, since 1 + 0 + 5 + 2 + 5 + 31 + 4 + 9 + 0 + 8 + 1 + 600 = 666.

It is a super-2 number, since 2×105253149081600² (a number of 29 digits) contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 2567149977580 + ... + 2567149977620.

Almost surely, 2^{105253149081600} is an apocalyptic number.

105253149081600 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 105253149081600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (222633281724672).

105253149081600 is an abundant number, since it is smaller than the sum of its proper divisors (340013414367744).

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

105253149081600 is an frugal number, since it uses more digits than its factorization.

105253149081600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 150 (or 95 counting only the distinct ones).

The product of its (nonzero) digits is 259200, while the sum is 45.

The spelling of 105253149081600 in words is "one hundred five trillion, two hundred fifty-three billion, one hundred forty-nine million, eighty-one thousand, six hundred".