What are the divisors of 8259?

1, 3, 2753, 8259

There is a total of 4 positive divisors.
The sum of these divisors is 11016.
The arithmetic mean is 2754.

4 odd divisors

1, 3, 2753, 8259

How to compute the divisors of 8259?

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 8259 by each of the numbers from 1 to 8259 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)

8259 / 1 = 8259 (the remainder is 0, so 1 is a divisor of 8259)
8259 / 2 = 4129.5 (the remainder is 1, so 2 is not a divisor of 8259)
8259 / 3 = 2753 (the remainder is 0, so 3 is a divisor of 8259)
...
8259 / 8258 = 1.0001210946961 (the remainder is 1, so 8258 is not a divisor of 8259)
8259 / 8259 = 1 (the remainder is 0, so 8259 is a divisor of 8259)

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 8259 (i.e. 90.879040487892). 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 $\frac{N}{d} = D$ )

8259 / 1 = 8259 (the remainder is 0, so 1 and 8259 are divisors of 8259)
8259 / 2 = 4129.5 (the remainder is 1, so 2 is not a divisor of 8259)
8259 / 3 = 2753 (the remainder is 0, so 3 and 2753 are divisors of 8259)
...
8259 / 89 = 92.797752808989 (the remainder is 71, so 89 is not a divisor of 8259)
8259 / 90 = 91.766666666667 (the remainder is 69, so 90 is not a divisor of 8259)