185640 has 128 divisors (see below), whose sum is σ = 725760. Its totient is φ = 36864.

The previous prime is 185621. The next prime is 185641. The reversal of 185640 is 46581.

Added to its reverse (46581) it gives a triangular number (232221 = T₆₈₁).

185640 = T₈₅ + T₈₆ + ... + T₁₁₉.

185640 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a nialpdrome in base 13.

It is a self number, because there is not a number n which added to its sum of digits gives 185640.

It is not an unprimeable number, because it can be changed into a prime (185641) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 10912 + ... + 10928.

It is an arithmetic number, because the mean of its divisors is an integer number (5670).

2¹⁸⁵⁶⁴⁰ is an apocalyptic number.

185640 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 185640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (362880).

185640 is an abundant number, since it is smaller than the sum of its proper divisors (540120).

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

185640 is a wasteful number, since it uses less digits than its factorization.

185640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 51 (or 47 counting only the distinct ones).

The product of its (nonzero) digits is 960, while the sum is 24.

The square root of 185640 is about 430.8596059043. The cubic root of 185640 is about 57.0458234165.

Adding to 185640 its reverse (46581), we get a triangular number (232221 = T₆₈₁).

The spelling of 185640 in words is "one hundred eighty-five thousand, six hundred forty".