36000 has 72 divisors (see below), whose sum is σ = 127764. Its totient is φ = 9600.

The previous prime is 35999. The next prime is 36007. The reversal of 36000 is 63.

36000 = 5^{3} + 6^{3} + ... + 19^{3}.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 24336 + 11664 = 156^2 + 108^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 15.

It is a zygodrome in base 15.

It is not an unprimeable number, because it can be changed into a prime (36007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 7198 + ... + 7202.

2^{36000} is an apocalyptic number.

36000 is a gapful number since it is divisible by the number (30) 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 36000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (63882).

36000 is an abundant number, since it is smaller than the sum of its proper divisors (91764).

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

36000 is a wasteful number, since it uses less digits than its factorization.

36000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 31 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 18, while the sum is 9.

The square root of 36000 is about 189.7366596101. The cubic root of 36000 is about 33.0192724889.

Adding to 36000 its reverse (63), we get a palindrome (36063).

Subtracting from 36000 its reverse (63), we obtain a cube (35937 = 33^{3}).

The spelling of 36000 in words is "thirty-six thousand", and thus it is an eban number.

Divisors: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 32 36 40 45 48 50 60 72 75 80 90 96 100 120 125 144 150 160 180 200 225 240 250 288 300 360 375 400 450 480 500 600 720 750 800 900 1000 1125 1200 1440 1500 1800 2000 2250 2400 3000 3600 4000 4500 6000 7200 9000 12000 18000 36000

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