8000 has 28 divisors (see below), whose sum is σ = 19812. Its totient is φ = 3200.

The previous prime is 7993. The next prime is 8009. The reversal of 8000 is 8.

8000 = 11^{3} + 12^{3} + ... + 14^{3}.

The cubic root of 8000 is 20.

It is a perfect power (a cube), and thus also a powerful number.

8000 is an esthetic number in base 6, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in 2 ways, for example, as 256 + 7744 = 16^2 + 88^2 .

It is a Harshad number since it is a multiple of its sum of digits (8).

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 10.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (8009) by changing a digit.

8000 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 3 ways as a sum of consecutive naturals, for example, 1598 + ... + 1602.

2^{8000} is an apocalyptic number.

8000 is a gapful number since it is divisible by the number (80) 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 8000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9906).

8000 is an abundant number, since it is smaller than the sum of its proper divisors (11812).

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

8000 is an equidigital number, since it uses as much as digits as its factorization.

8000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 27 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 8, while the sum is 8.

The square root of 8000 is about 89.4427191000.

The spelling of 8000 in words is "eight thousand".

Divisors: 1 2 4 5 8 10 16 20 25 32 40 50 64 80 100 125 160 200 250 320 400 500 800 1000 1600 2000 4000 8000

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