6000 has 40 divisors (see below), whose sum is σ = 19344. Its totient is φ = 1600.

The previous prime is 5987. The next prime is 6007. The reversal of 6000 is 6.

6000 = T_{19} + T_{20} + ... +
T_{34}.

6000 is an esthetic number in base 11, because in such base its adjacent digits differ by 1.

It is a tau number, because it is divible by the number of its divisors (40).

It is a Harshad number since it is a multiple of its sum of digits (6).

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

It is a plaindrome in base 14.

It is a nialpdrome in base 10.

It is a zygodrome in base 14.

It is a self number, because there is not a number *n* which added to its sum of digits gives 6000.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (6007) by changing a digit.

6000 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1198 + ... + 1202.

2^{6000} is an apocalyptic number.

6000 is a gapful number since it is divisible by the number (60) 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 6000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9672).

6000 is an abundant number, since it is smaller than the sum of its proper divisors (13344).

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

6000 is a wasteful number, since it uses less digits than its factorization.

6000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 26 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 6, while the sum is 6.

The square root of 6000 is about 77.4596669241. The cubic root of 6000 is about 18.1712059283.

The spelling of 6000 in words is "six thousand", and thus it is an eban number.

Divisors: 1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 40 48 50 60 75 80 100 120 125 150 200 240 250 300 375 400 500 600 750 1000 1200 1500 2000 3000 6000

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