105735528900 has 135 divisors (see below), whose sum is σ = 342847705431. Its totient is φ = 28188336960.

The previous prime is 105735528869. The next prime is 105735528937. The reversal of 105735528900 is 9825537501.

The square root of 105735528900 is 325170.

It is a perfect power (a square), and thus also a powerful number.

105735528900 is a `hidden beast` number, since 1 + 0 + 5 + 7 + 3 + 552 + 8 + 90 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 65266964676 + 40468564224 = 255474^2 + 201168^2 .

It is a tau number, because it is divible by the number of its divisors (135).

It is a super-2 number, since 2×105735528900² (a number of 23 digits) contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 29263494 + ... + 29267106.

Almost surely, 2^105735528900 is an apocalyptic number.

105735528900 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

105735528900 is the 325170-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105735528900

105735528900 is an abundant number, since it is smaller than the sum of its proper divisors (237112176531).

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

105735528900 is an frugal number, since it uses more digits than its factorization.

105735528900 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7252 (or 3623 counting only the distinct ones).

The product of its (nonzero) digits is 378000, while the sum is 45.

The spelling of 105735528900 in words is "one hundred five billion, seven hundred thirty-five million, five hundred twenty-eight thousand, nine hundred".