105713664000 has 512 divisors, whose sum is σ = 402395385600. Its totient is φ = 24143462400.

The previous prime is 105713663989. The next prime is 105713664013. The reversal of 105713664000 is 466317501.

It is a tau number, because it is divible by the number of its divisors (512).

It is a super-2 number, since 2×105713664000² (a number of 23 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 86015386 + ... + 86016614.

Almost surely, 2^105713664000 is an apocalyptic number.

105713664000 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 105713664000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (201197692800).

105713664000 is an abundant number, since it is smaller than the sum of its proper divisors (296681721600).

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

105713664000 is an frugal number, since it uses more digits than its factorization.

105713664000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1284 (or 1246 counting only the distinct ones).

The product of its (nonzero) digits is 15120, while the sum is 33.

The spelling of 105713664000 in words is "one hundred five billion, seven hundred thirteen million, six hundred sixty-four thousand".