What are the divisors of 8279?

1, 17, 487, 8279

There is a total of 4 positive divisors.
The sum of these divisors is 8784.
The arithmetic mean is 2196.

4 odd divisors

1, 17, 487, 8279

How to compute the divisors of 8279?

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 8279 by each of the numbers from 1 to 8279 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)

8279 / 1 = 8279 (the remainder is 0, so 1 is a divisor of 8279)
8279 / 2 = 4139.5 (the remainder is 1, so 2 is not a divisor of 8279)
8279 / 3 = 2759.6666666667 (the remainder is 2, so 3 is not a divisor of 8279)
...
8279 / 8278 = 1.0001208021261 (the remainder is 1, so 8278 is not a divisor of 8279)
8279 / 8279 = 1 (the remainder is 0, so 8279 is a divisor of 8279)

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 8279 (i.e. 90.989010325423). 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 $\frac{N}{d} = D$ )

8279 / 1 = 8279 (the remainder is 0, so 1 and 8279 are divisors of 8279)
8279 / 2 = 4139.5 (the remainder is 1, so 2 is not a divisor of 8279)
8279 / 3 = 2759.6666666667 (the remainder is 2, so 3 is not a divisor of 8279)
...
8279 / 89 = 93.022471910112 (the remainder is 2, so 89 is not a divisor of 8279)
8279 / 90 = 91.988888888889 (the remainder is 89, so 90 is not a divisor of 8279)