What are the divisors of 8079?

1, 3, 2693, 8079

There is a total of 4 positive divisors.
The sum of these divisors is 10776.
The arithmetic mean is 2694.

4 odd divisors

1, 3, 2693, 8079

How to compute the divisors of 8079?

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 8079 by each of the numbers from 1 to 8079 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)

8079 / 1 = 8079 (the remainder is 0, so 1 is a divisor of 8079)
8079 / 2 = 4039.5 (the remainder is 1, so 2 is not a divisor of 8079)
8079 / 3 = 2693 (the remainder is 0, so 3 is a divisor of 8079)
...
8079 / 8078 = 1.0001237930181 (the remainder is 1, so 8078 is not a divisor of 8079)
8079 / 8079 = 1 (the remainder is 0, so 8079 is a divisor of 8079)

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 8079 (i.e. 89.883257617868). 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 $\frac{N}{d} = D$ )

8079 / 1 = 8079 (the remainder is 0, so 1 and 8079 are divisors of 8079)
8079 / 2 = 4039.5 (the remainder is 1, so 2 is not a divisor of 8079)
8079 / 3 = 2693 (the remainder is 0, so 3 and 2693 are divisors of 8079)
...
8079 / 88 = 91.806818181818 (the remainder is 71, so 88 is not a divisor of 8079)
8079 / 89 = 90.775280898876 (the remainder is 69, so 89 is not a divisor of 8079)