105786960400 has 180 divisors, whose sum is σ = 281252506500. Its totient is φ = 38207206400.

The previous prime is 105786960379. The next prime is 105786960401. The reversal of 105786960400 is 4069687501.

It can be written as a sum of positive squares in 6 ways, for example, as 8440464384 + 97346496016 = 91872^2 + 312004^2 .

It is a super-2 number, since 2×105786960400² (a number of 23 digits) contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (105786960401) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 7204266 + ... + 7218934.

It is an arithmetic number, because the mean of its divisors is an integer number (1562513925).

Almost surely, 2^105786960400 is an apocalyptic number.

105786960400 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 105786960400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (140626253250).

105786960400 is an abundant number, since it is smaller than the sum of its proper divisors (175465546100).

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

105786960400 is a wasteful number, since it uses less digits than its factorization.

105786960400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 14858 (or 14836 counting only the distinct ones).

The product of its (nonzero) digits is 362880, while the sum is 46.

The spelling of 105786960400 in words is "one hundred five billion, seven hundred eighty-six million, nine hundred sixty thousand, four hundred".