36288 has 70 divisors (see below), whose sum is σ = 122936. Its totient is φ = 10368.

The previous prime is 36277. The next prime is 36293. The reversal of 36288 is 88263.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits.

Its product of digits (2304) is a multiple of the sum of its prime divisors (12).

It is a nialpdrome in base 6 and base 14.

It is a zygodrome in base 6.

It is a congruent number.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 36288.

It is an unprimeable number.

36288 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 5181 + ... + 5187.

2^{36288} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 36288, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (61468).

36288 is an abundant number, since it is smaller than the sum of its proper divisors (86648).

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

36288 is an equidigital number, since it uses as much as digits as its factorization.

36288 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 31 (or 12 counting only the distinct ones).

The product of its digits is 2304, while the sum is 27.

The square root of 36288 is about 190.4940943967. The cubic root of 36288 is about 33.1070901166.

Adding to 36288 its sum of digits (27), we get a triangular number (36315 = T_{269}).

It can be divided in two parts, 36 and 288, that added together give a square (324 = 18^{2}).

The spelling of 36288 in words is "thirty-six thousand, two hundred eighty-eight".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 32 36 42 48 54 56 63 64 72 81 84 96 108 112 126 144 162 168 189 192 216 224 252 288 324 336 378 432 448 504 567 576 648 672 756 864 1008 1134 1296 1344 1512 1728 2016 2268 2592 3024 4032 4536 5184 6048 9072 12096 18144 36288

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