What are the divisors of 8013?

1, 3, 2671, 8013

There is a total of 4 positive divisors.
The sum of these divisors is 10688.
The arithmetic mean is 2672.

4 odd divisors

1, 3, 2671, 8013

How to compute the divisors of 8013?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 8013 by each of the numbers from 1 to 8013 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

8013 / 1 = 8013 (the remainder is 0, so 1 is a divisor of 8013)
8013 / 2 = 4006.5 (the remainder is 1, so 2 is not a divisor of 8013)
8013 / 3 = 2671 (the remainder is 0, so 3 is a divisor of 8013)
...
8013 / 8012 = 1.0001248127808 (the remainder is 1, so 8012 is not a divisor of 8013)
8013 / 8013 = 1 (the remainder is 0, so 8013 is a divisor of 8013)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 8013 (i.e. 89.515361810138). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

8013 / 1 = 8013 (the remainder is 0, so 1 and 8013 are divisors of 8013)
8013 / 2 = 4006.5 (the remainder is 1, so 2 is not a divisor of 8013)
8013 / 3 = 2671 (the remainder is 0, so 3 and 2671 are divisors of 8013)
...
8013 / 88 = 91.056818181818 (the remainder is 5, so 88 is not a divisor of 8013)
8013 / 89 = 90.033707865169 (the remainder is 3, so 89 is not a divisor of 8013)