What are the divisors of 8061?

1, 3, 2687, 8061

There is a total of 4 positive divisors.
The sum of these divisors is 10752.
The arithmetic mean is 2688.

4 odd divisors

1, 3, 2687, 8061

How to compute the divisors of 8061?

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 8061 by each of the numbers from 1 to 8061 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)

8061 / 1 = 8061 (the remainder is 0, so 1 is a divisor of 8061)
8061 / 2 = 4030.5 (the remainder is 1, so 2 is not a divisor of 8061)
8061 / 3 = 2687 (the remainder is 0, so 3 is a divisor of 8061)
...
8061 / 8060 = 1.0001240694789 (the remainder is 1, so 8060 is not a divisor of 8061)
8061 / 8061 = 1 (the remainder is 0, so 8061 is a divisor of 8061)

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 8061 (i.e. 89.783071901111). 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 $\frac{N}{d} = D$ )

8061 / 1 = 8061 (the remainder is 0, so 1 and 8061 are divisors of 8061)
8061 / 2 = 4030.5 (the remainder is 1, so 2 is not a divisor of 8061)
8061 / 3 = 2687 (the remainder is 0, so 3 and 2687 are divisors of 8061)
...
8061 / 88 = 91.602272727273 (the remainder is 53, so 88 is not a divisor of 8061)
8061 / 89 = 90.573033707865 (the remainder is 51, so 89 is not a divisor of 8061)