165938145609600 has 5760 divisors, whose sum is σ = 811829042830080. Its totient is φ = 32700107980800.

The previous prime is 165938145609581. The next prime is 165938145609601. The reversal of 165938145609600 is 6906541839561.

165938145609600 is a `hidden beast` number, since 1 + 6 + 5 + 9 + 3 + 8 + 1 + 4 + 560 + 9 + 60 + 0 = 666.

165938145609600 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (5760).

It is a super-2 number, since 2×165938145609600² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (165938145609601) by changing a digit.

It is a polite number, since it can be written in 719 ways as a sum of consecutive naturals, for example, 1266703401535 + ... + 1266703401665.

It is an arithmetic number, because the mean of its divisors is an integer number (140942542158).

Almost surely, 2^{165938145609600} is an apocalyptic number.

165938145609600 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 165938145609600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (405914521415040).

165938145609600 is an abundant number, since it is smaller than the sum of its proper divisors (645890897220480).

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

165938145609600 is an equidigital number, since it uses as much as digits as its factorization.

165938145609600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 232 (or 178 counting only the distinct ones).

The product of its (nonzero) digits is 41990400, while the sum is 63.

The spelling of 165938145609600 in words is "one hundred sixty-five trillion, nine hundred thirty-eight billion, one hundred forty-five million, six hundred nine thousand, six hundred".