3000 has 32 divisors (see below), whose sum is σ = 9360. Its totient is φ = 800.

The previous prime is 2999. The next prime is 3001. The reversal of 3000 is 3.

Added to its reverse (3) it gives a triangular number (3003 = T_{77}).

It is an interprime number because it is at equal distance from previous prime (2999) and next prime (3001).

It is an ABA number since it can be written as A⋅B^{A}, here for A=3, B=10.

It is a Harshad number since it is a multiple of its sum of digits (3).

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 11, base 13 and base 14.

It is a nialpdrome in base 5, base 10, base 15 and base 16.

It is a zygodrome in base 5, base 11 and base 14.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (3001) by changing a digit.

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, 598 + ... + 602.

2^{3000} is an apocalyptic number.

3000 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 3000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4680).

3000 is an abundant number, since it is smaller than the sum of its proper divisors (6360).

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

3000 is a wasteful number, since it uses less digits than its factorization.

3000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 24 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 3, while the sum is 3.

The square root of 3000 is about 54.7722557505. The cubic root of 3000 is about 14.4224957031.

The spelling of 3000 in words is "three thousand", and thus it is an iban number.

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

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